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Robust H
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guaranteed cost time-varying formation tracking problems for high-order multiagent systems with external disturbances and time-varying delays are considered. It is required that the followers' states need to track the leader's state and to actualize the desired time-varying formation simultaneously. First, this paper devises a linear time-varying formation tracking protocol considering the effects of the delays constituted by the neighboring information. Then, an integral linear quadratic cost function constructed by the control input constraint and the formation tracking error constraint is utilized to analyze the suboptimal robust H
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guaranteed cost time-varying formation tracking performance. Third, sufficient conditions for actualizing the guaranteed cost time-varying formation tracking with H
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disturbance attenuation performance are derived, and the conditions for the feasible time-varying formation tracking are raised. To obtain the gain matrix of the protocol, only four linear matrix inequalities are required to be solved. Finally, a numerical simulation example reveals the effectiveness of the acquired results, where five agents achieve the robust H
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guaranteed cost time-varying formation tracking.

To read the full-text of this research,

you can request a copy directly from the authors.

... A total restriction function associated with the linear quadratic regulator was proposed in 20 , where the optimal cooperation can be achieved when the information topology is complete. In [21][22][23] , the guaranteed-cost strategy was proposed, where the different upper bounds of the total energy restriction were obtained, but the error between these bounds and the minimum bound cannot be determined. The limited-budget strategy was presented in 24 , where an upper bound of the energy restriction was specified in advance. ...

... The first aspect is that this article realizes the distributed formation control and the minimum-energy restriction simultaneously. However, the guaranteed-cost strategy and the limited-budget strategy in [22][23][24] cannot minimize the total energy restriction of all agents as a whole. The second aspect is that the effects of the interaction silence on the formation control with the minimum-energy restriction are handled by introducing two inhibition parameters and the interaction silence rate in this article, and a specific condition about the interaction silence rate is constructed to constrain the divergent quantity during the interaction silence subsegment. ...

... The second aspect is that the effects of the interaction silence on the formation control with the minimum-energy restriction are handled by introducing two inhibition parameters and the interaction silence rate in this article, and a specific condition about the interaction silence rate is constructed to constrain the divergent quantity during the interaction silence subsegment. However, the influence of the interaction silence on the minimum energy restriction was not considered in [22][23][24] . The third aspect is that the explicit expression of the whole motion trajectory for the minimum-energy-restriction formation is determined, where the effects of the initial states of all agents and formation control vectors are depicted and it is shown that the interaction silence does not impact the formation whole motion trajectory, which were not settled in [22][23][24] . ...

The minimum-energy formation strategy for interconnected networks with distributed formation protocols is persented, where the impacts of the total energy restriction and the interaction silence are analyzed, respectively. The critical feature of this article is that the distributed formation and the minimum-energy restriction are realized simultaneously, and the total energy restriction is minimum in the sense of the linear matrix inequality. However, the guaranteed-cost formation strategy and the limited-budget formation strategy cannot guarantee that the energy restriction is minimum. Firstly, sufficient conditions for minimum-energy-restriction formation without the interaction silence are proposed, which can be solved by a specific optimization approach in terms of the linear matrix inequality, and the formation whole motion trajectory is determined, which is closely related to the average of the initial states of all agents and formation control vectors. Then, minimum-energy-restriction formation criteria for interconnected systems with the interaction silence are proposed by introducing two inhibition parameters and the interaction silence rate. Finally, two simulation examples are performed to illustrate the effectiveness of theoretical analyses.

... Distributed leader-based H ∞ consensus of linear MASs under switching topologies with permanent occurrence of a DST and a relative state feedback approach is discussed in [32]. Robust H ∞ time varying tracking for high-order MASs has been discussed in [33] under time-varying delays, disturbances, and fixed topology. These studies demonstrate that robustness of consensus control schemes is needed for dealing with unwanted effects of disturbances for convergence of the consensus error. ...

... The robust time varying formation tracking for linear MASs is considered in [34] under disturbances, parameter uncertainties, and fixed topology. In contrast to [31][32][33][34], we consider H ∞ consensus OSL non-linear MASs under switching topologies with disturbances in followers. The robustness issues for the consensus control under disturbances and switching of communication topologies is an important research area, which can assure consensus between MASs in a physical environment. ...

... where κ = q 0 N 0 ln κ/ p 0 and β = β − ln κ/τ o . Thus, (33) means that the consensus error between states of the leader and followers reaches to the zero, that is to say δ t → 0, under zero disturbances. ...

This paper deals with the multiple Lyapunov functions approach for the robust leader-following consensus of one-sided Lipschitz (OSL) multiagents, connected via switching topologies under external disturbances. Disturbances have been accounted for followers, connected via a directed graph with a spanning tree from the leader root. We stipulate two consensus protocols, based on the absence or existence of norm-bounded reference input to the leader, and provide matrix inequalities for designing the parameters of consensus controllers. In the presence of bounded disturbances, our protocol ensures consensus criterion for minimization of the effect of disturbances to the consensus error between the leader and followers. A remedy for striking robustness against external perturbations has been provided in the present work in contrast to the conventional consensus schemes on OSL agents. Switching OSL mobile agents and aircraft carriers consisting of a leader and five followers have been simulated in the existence of reference input and disturbances to demonstrate the empirical proficiency of the consensus protocol schemes.

... Inspired by the guaranteed-cost synchronization control for swarm systems addressed in [30], Wang et al. [31] investigated guaranteedperformance formation control with limited communication. Yu et al. [32] discussed guaranteed-performance formation control for swarm systems with time-varying delays and unknown disturbances and presented the formation control criteria on the basis of the linear matrix inequality, where no approach was proposed to determine the specific structure of the guaranteed-performance cost. Moreover, the associated formation control criteria in [31,32] are associated with the global information of swarm systems, such as the Laplacian matrix of the communication network or its nonzero eigenvalues; that is, those criteria are not fully distributed since gain matrices may be changed when some agents are removed or some agents are added in swarm systems. ...

... Yu et al. [32] discussed guaranteed-performance formation control for swarm systems with time-varying delays and unknown disturbances and presented the formation control criteria on the basis of the linear matrix inequality, where no approach was proposed to determine the specific structure of the guaranteed-performance cost. Moreover, the associated formation control criteria in [31,32] are associated with the global information of swarm systems, such as the Laplacian matrix of the communication network or its nonzero eigenvalues; that is, those criteria are not fully distributed since gain matrices may be changed when some agents are removed or some agents are added in swarm systems. As far as we know, the synchronization-based guaranteed-performance formation design problem for swarm systems with the fully distributed control strategy is still not comprehensively studied. ...

... Firstly, synchronization-based guaranteed-performance formation criteria are fully distributed; that is, the gain matrix design is independent of the global information of communication networks of swarm systems. In [31,32], the formation performance among neighboring agents can only be regulated. irdly, the whole motion of a swarm system depends on the average of initial values of velocity-similar states and position-similar states and formation control vectors. ...

Guaranteed-performance formation control for swarm systems with the second-order dynamics is investigated based on the synchronization control strategy. Firstly, a new formation protocol is presented, where the weights of connected edges are adaptively regulated and the performance constraint is imposed. Then, on the basis of the Riccati inequality, sufficient conditions for synchronization-based guaranteed-performance formation are proposed, and an explicit expression of the guaranteed-performance cost is shown, where it is fully distributed to design gain matrices of the formation protocol in the sense that it is independent of global information of swarm systems. Moreover, the whole motion of a swarm system is determined, which is associated with initial states of all agents and formation control vectors. Finally, two numerical examples are shown to demonstrate theoretical conclusions, where the static whole motion and the dynamic whole motion are considered, respectively.

... Motivated by the guaranteed-cost consensus discussed in [33], Wang et al. [34] investigated guaranteed-performance time-varying formation with communication constraints, where an upper bound of the performance cost was determined, but energy consumptions were not dealt with and the performance cost cannot be given previously. Yu et al. [35] addressed guaranteed-cost timevarying formation with unknown external disturbances and time delays and proposed the associated criteria based on the linear matrix inequality tool, where the explicit expression of the performance cost was not determined. Especially, the upper bound of the performance cost cannot be given previously. ...

... Firstly, the current paper focuses on energy-constraint formation control; that is, the whole energy supply is given previously. The impacts of energy constraints on formation control were not considered in [21]- [29] and the whole energy supply cannot be limited previously in [34] and [35]. Secondly, the relationships between the whole energy supply and the matrix variable are determined, which introduce the whole energy supply into formation design and analysis criteria. ...

... Secondly, the relationships between the whole energy supply and the matrix variable are determined, which introduce the whole energy supply into formation design and analysis criteria. Formation control approaches with performance constraints in [34] and [35] did not determined the explicit interaction relationships. Thirdly, a new two-step transformation approach is proposed to deal with asymmetric structure properties of leader-following switching interaction topologies and to unify leaderless and leader-following cases into the same framework. ...

The current paper investigates energy-constraint formation design and analysis problems for multiagent systems with two types of switching interaction topologies; that is, leaderless ones and leader-following ones. Firstly, a new formation control protocol with switching interaction topologies is shown, where the whole energy supply is limited previously. Then, by constructing the relationship of the whole energy supply and the matrix variable, sufficient conditions for leaderless energy-constraint formation design and analysis are respectively presented by the linear matrix inequality tool. Furthermore, an approach is proposed to determine an explicit expression of the formation center function, which determines the macroscopic motion of a multiagent system as a whole and consists of two parts: the initial state term and the formation function term. Moreover, main conclusions of leaderless energy-constraint formation are extended into leader-following multiagent systems by a new two-step transformation approach, where the asymmetric structure feature of leader-following switching interaction topologies is well dealt with. Finally, two numerical examples are provided to demonstrate the effectiveness of main conclusions.

... Then, analyze the inequality (27). One has ...

... Thus, (27) holds. It follows that ...

In this paper, the H∞ and H2 time-varying formation tracking problems for multi-agent systems with directed topologies in the presence of external disturbances are investigated. The followers need to achieve the desired time-varying formation during movement and simultaneously track the state trajectory generated by the leader. First, a distributed consensus protocol based on the local state information of neighbors of the agents for solving H∞ and H2 time-varying formation tracking problems are proposed without utilizing global information about the entire agents. The conditions to achieve H∞ and H2 time-varying formation tracking in the presence of external disturbances are suggested respectively. Then, to determine the parameters of the designed protocol which satisfy suitable conditions, algorithms for H∞ and H2 time-varying formation tracking in the form of pseudo-code are presented, respectively. Furthermore, the proofs of the proposed theorems are derived by utilizing algebraic graph theory and Lyapunov analysis theory tools to demonstrate the closed-loop stability of the system in the presence of external disturbances. Finally, the usefulness and effectiveness of the approaches proposed are demonstrated by numerical simulation examples.

... 29-31, state formation tracking problems were investigated, where energy consumption was not considered, but being very important for engineering applications of networked systems. Dong et al. 32 studied guaranteed cost formation tracking, where the energy supply was not determined previously. To the best of our knowledge, output formation tracking for networked systems with the limited energy and the aperiodic silence is still open. ...

... The third one is that the internal influence mechanism of the limited energy on output formation is analyzed and the relationship between the matrix variable and the limited energy is constructed in the current paper. The impacts of the energy constraint were not considered in Ref. [29][30] and an upper bound of the guaranteed cost was determined in Ref. 32, but this upper bound cannot be given previously and their methods are no longer valid to deal with networked systems with the limited energy. ...

For leader-following networked systems with the topology switching and the aperiodic silence, limited-energy output formation tracking problems are investigated. Firstly, a new output formation tracking control protocol is proposed, which contains two components associated with the communication interactions between the leader and tracking intelligent agents and the communication interactions among tracking intelligent agents, respectively, and the aperiodic silence, the topology switching and the energy constraint index is introduced properly. Then, a two-step transformation method is presented to separate the whole dynamics of a networked system into the relative dynamics between the leader and tracking intelligent agents and the dynamics of the leader, and sufficient conditions for limited-energy output formation tracking for networked systems with limited energy and aperiodic silence are presented, which are extended into networked systems without the aperiodic silence. Especially, a partition checking algorithm is presented to check limited-energy output formation tracking design criteria. Finally, a numerical example is illustrated to demonstrate the validness of theoretical results.

... munication delay and input delay, a truncated predictor feedback approach was proposed to solve the consensus problem of NMASs in [15], and the proof that relaxed the restrictions of delays was given. For NMASs with second-order dynamics, two-channel time-varying delays in [17] were taken into account, but similar to [16] and [18], the delays at each instant for all agents were treated conservatively as a uniform value. In practice, the delays generally vary from agent to agent in specific application scenarios even if all the agents are homogeneous. ...

... Compared with the stochastic system approach [10], the Lyapunov-Krasovskii function approach [16][17][18][19] and other approaches mentioned above where the communication constraints were usually handled in a passive way, the networked predictive control (NPC) approach [11][12][13][14] has a distinct superiority, that is, the communication constraints can be compensated actively by using model-based predictive control methods. Furthermore, if each agent and its model matche exactly, the NPC approach can obtain the same control performance as the case where there are no communication constraints. ...

In this paper, we discuss the cooperative output tracking problem for networked multi-agent systems (NMASs) with plant-model mismatch as well as random communication constraints in the forward and feedback channels of each agent. In order to compensate actively for random communication constraints, that is, network-induced delays and packet dropouts, an incremental networked predictive control scheme based on a state observer is proposed, which consists of a data buffer, an incremental networked predictor, and a network delay compensator. For both the plant-model mismatch case and the plant-model match case, the stability conditions of resulting closed-loop NMASs are derived, respectively. Using the proposed method, the simulation results for three DC motor systems are presented to indicate that desired tracking performance can be achieved. © 2021 The Authors. IET Control Theory & Applications published by John Wiley & Sons Ltd on behalf of The Institution of Engineering and Technology

... Cao and Ren [21] modeled the energy constraint as an optimal or suboptimal problem by a global index function and showed that optimal formation control can be realized under the condition that the communication topology is complete; that is, all agents in a networked system communicate with each other. In [22] and [23], sufficient conditions for guaranteed-cost formation were proposed, where guaranteed-cost formation realizes suboptimal formation control. In [21]- [23], state formation instead of output formation was addressed. ...

... For l = 0, one can see by (22) and (23) that ...

For high-order linear networked systems with switching topologies and the random communication silence, energy-constraint output formation problems are investigated. Firstly, the dynamics associated with the coordinated output is decomposed from the whole dynamics of each intelligent agent and a new control protocol is constructed on the basis of the coordinated outputs and the protocol states of neighboring intelligent agents, where switching topologies, the energy constraint and the random communication silence are contained. Then, by introducing the silent rate and the dwell time, the impacts of the random communication silence and switching topologies are dealt with and sufficient conditions for energy-constraint output formation design and analysis are proposed, where the output formation feasible conditions are required to guarantee the output formation achievement property. Especially, an explicit expression of the output formation center function is determined, which depicts the whole motion of a networked system when energy-constraint output formation is achieved. Finally, a numerical example is given to demonstrate theoretical conclusions.

... Similar to the guaranteed-cost control of isolated systems, the whole guaranteed-cost function was constructed on the basis of the integral principle in [27,28], where sufficient conditions for the guaranteed-cost formation were proposed via the linear matrix inequality tool and the nonzero eigenvalues of the Laplacian matrix of the communication topology. Yu et al. [29] presented the guaranteed-cost time-varying formation criteria for swarm systems with external disturbances and time-varying delays, but they did not give an approach to determine the upper bound of the performance function. Especially, it should be pointed out that the whole energy supply of a swarm system was assumed to be infinite when distributed formation control was carried out in [27][28][29]. ...

... Yu et al. [29] presented the guaranteed-cost time-varying formation criteria for swarm systems with external disturbances and time-varying delays, but they did not give an approach to determine the upper bound of the performance function. Especially, it should be pointed out that the whole energy supply of a swarm system was assumed to be infinite when distributed formation control was carried out in [27][28][29]. Actually, the whole energy supply is usually limited for practical swarm systems and its impacts on time-varying formation control are critically important. To the best of our knowledge, the design and analysis problems of time-varying formation tracking for high-order linear time-variant swarm systems with the limited energy and fixed topologies are still open and are not comprehensively discussed. ...

The current paper investigates design and analysis problems of formation tracking for high-order linear time-invariant swarm systems, where communication topologies among agents have leader-following structures and the whole energy supply is limited. Firstly, the communication topology of a swarm system is depicted by a directed graph with a spanning tree, where the communication channels from the leader to followers are directional and the communication channels among followers are bidirectional, and a new formation tracking protocol with an energy integral term and a given upper bound is proposed to achieve formation tracking with the limited energy. Then, sufficient conditions for time-varying formation tracking design and analysis with the limited energy are presented, respectively, which include two/three linear matrix inequality constraints associated with the maximum and minimum nonzero eigenvalues of the Laplacian matrix of a communication topology. Especially, time-invariant formation tracking criteria are further deduced. Finally, two numerical examples are revealed to verify main theoretical conclusions.

... In [30,31], the concept of the guaranteed-cost control was introduced to analyze the impacts of the energy constraint and gave several guaranteed-cost formation criteria. Yu et al. [32] investigated the guaranteed-cost time-varying formation control problem, where the impacts of unknown external disturbances and time delays were considered and the guaranteed-cost timevarying formation criteria were proposed, but the performance cost cannot be determined by their methods. In [30][31][32], the energy supply of a swarm system as a whole cannot be given previously. ...

... Yu et al. [32] investigated the guaranteed-cost time-varying formation control problem, where the impacts of unknown external disturbances and time delays were considered and the guaranteed-cost timevarying formation criteria were proposed, but the performance cost cannot be determined by their methods. In [30][31][32], the energy supply of a swarm system as a whole cannot be given previously. However, the whole energy supply is usually limited in practical swarm systems and it is critically important to discuss the influences of the whole energy supply on time-varying formation design and analysis problems. ...

This paper discusses limited-budget time-varying formation design and analysis problems for a high-order linear swarm system with a fixed communication topology. Firstly, the communication topology among agents is modeled as an undirected and connected graph, and a new formation control protocol with an energy integral term is proposed to realize formation control and to guarantee the practical energy assumption is less than the limited energy budget. Then, by the matrix inequality tool, sufficient conditions for limited-budget formation design and analysis are proposed, respectively, which are scalable and checkable since they are independent of the number of agents of a swarm system and can be transformed into linear matrix inequality constraints. Moreover, an explicit expression of the formation center function is given, which contains the formation function part and the cooperative state part and is not associated with the derivatives of the formation functions. Finally, a numerical simulation is shown to demonstrate the effectiveness of theoretical results.

... Therefore, the guaranteed performance control of multi-agent systems has received much attention recently [40]. Robust H ∞ guaranteed cost time-varying formation tracking problem for high-order multi-agent systems was considered in [41]. In [42], guaranteed-performance time-varying formation control for swarm systems was investigated. ...

This paper is concerned with event-triggered guaranteed-cost bipartite formation control of multi-agent systems with antagonistic interactions. In order to save the limited network communication bandwidth of multi-agent systems, event-triggered sampled-data transmission strategy is adopted. Event conditions are designed for both leader and followers to reduce the frequency of state transmission more effectively. According to the event-triggered sampled-data of the leader and followers, bipartite formation controllers are designed for followers. By using the event conditions and the Lyapunov method, the sufficient conditions for the realization of bipartite formation and guaranteed-cost bipartite formation are obtained in terms of linear matrix inequality, respectively. Finally, the effectiveness of the theoretical results is demonstrated by numerical examples.

... It should be pointed out that the derivative upper bound μ is an important factor in the exponential stability. Generally speaking, μ is usually limited to less than 1 (see [17,30,31]). When time delays are defined in this study, μ is not restricted and more general, namely, time delays can change rapidly or slowly over time. ...

This study is related to the exponential synchronization problem of stochastic neural networks. A dynamic model of master-slave neural networks is established, which contains time-varying delays and Lévy noises. The main purpose is to enable the slave system to follow the master system under the condition of limited communication capacity. Both the master system and the slave system are affected by random noises. Some sufficient conditions are given by means of linear matrix inequality methods which are established by applying Lyapunov functional together with the generalized Dynkin’s formula. Furthermore, a discrete event-triggered control is adopted in master-slave systems, which not only reduces the transmission resources but also avoids the Zeno phenomenon. At last, a numerical example is provided to verify the usefulness of judgment conditions in this study.

... Since then, some GCC algorithms have been designed for quadrotor unmanned aerial vehicle (UAV) [26], high-train movement [27], and multi-agent systems [28]. Consider the influences of the disturbances and model uncertainties, GCC strategies with H ∞ performance were proposed for various systems [29][30][31][32]. ...

In this paper, a decentralized guaranteed cost H∞ control strategy is proposed for large‐scale web‐winding systems with uncertain and time‐varying parameters. First, the large‐scale web‐winding system is viewed as a synthetic system composed of several dynamic subsystems, and interval matrix is used to deal with parameter uncertainties and the changes of set point. Second, a decentralized guaranteed cost control (DGCC) is developed to achieve the track goal, and guarantees that a cost function defined for the control system has an upper bound. Furthermore, an optimal DGCC (ODGCC) is designed to minimize the upper bound. Third, H∞ control strategy is incorporated in the DGCC to increase closed‐loop system robustness to parameter uncertainties and external disturbances. Finally, some simulation and experiments are performed on a three‐motor web‐winding system to verify the effectiveness of the presented control methods.

... In fact, several tasks may benefit from solutions of formation control, such as load transportation with cooperative robots to move flexible payloads [10]. Different formation control scenarios have been investigated such as the ones incorporating, but not limited to, time-varying formations [11,12,13,14], formations with multiple leaders [15,16,17], switching network topologies [18,19,20], time-delays [21,22], etc. Stochastic switching topologies with time-varying delays have also been considered in [23]. ...

This paper presents a solution based on dual quaternion algebra to the general problem of pose (i.e., position and orientation) consensus for systems composed of multiple rigid-bodies. The dual quaternion algebra is used to model the agents’ poses and also in the distributed control laws, making the proposed technique easily applicable to time-varying formation control of general robotic systems. The proposed pose consensus protocol has guaranteed convergence when the interaction among the agents is represented by directed graphs with directed spanning trees, which is a more general result when compared to the literature on formation control. In order to illustrate the proposed pose consensus protocol and its extension to the problem of formation control, we present a numerical simulation with a large number of free-flying agents and also an application of cooperative manipulation by using real mobile manipulators.

In recent years, cooperative control has shown potential value in practical applications, and the design of an appropriate consensus protocol has received increasing attention from various scientific communities. First of all, the research background of multi-agent systems (MASs) is described and extends to the concept, research status and graph theory, in which the different definition methods of consensus protocol are derived. Afer this, the developments of current consensus protocols are analyzed and summarized from the view of topology switching, finite time, communication delay and so on. Then, three classical control methods of formation control in heterogeneous multi-agent are introduced: leader-following, behavior-based, and virtual structure. Finally, the unsolved problems and the future research direction are discussed.

The secure consensus problem of multiagent systems with fixed topology and external disturbances is investigated in this paper. Along with external disturbances, the studied multiagent system is also subjected to denial-of-service (DoS) attacks. First, some graph-based Lyapunov functions are presented for the robust consensus analysis. Second, the duration and attack frequency are introduced to quantitatively analyze the DoS attacks’ effects on the consensus. Third, the gain of the controller is acquired by solving an algebraic Riccati equation (ARE), which can always be guaranteed compared with solving linear matrix inequalities (LMIs). Finally, a numerical simulation of a microgrid test system is provided to demonstrate the effectiveness of the proposed strategy.

In this article, time-varying group formation (TVGF) tracking problems for general linear multiagent systems (GLMASs) with switching interaction topologies are investigated. Different from previous studies, a novel TVGF tracking approach is proposed, where all agents are divided into three types: the virtual leader, the group leader, and the follower. The virtual leader is designed to assign the trajectory of GLMASs. Subgroups can be interacted with each other by cooperation among group leaders such that the relative configuration between different groups can be adjusted simultaneously. The followers in each group can achieve time-varying subformations. Moreover, under the influence of external disturbances and switching topologies, based on the distributed observer, two different distributed adaptive control protocols are constructed without using any global information such as the eigenvalue of the Laplacian matrix related to the communication topologies, the upper boundness of the leader’s input, and so on. The algorithms to determine parameters of control protocols are also presented. Furthermore, the closed-loop stability of GLMASs is proven by the Lyapunov theory. Finally, numerical simulations are given to verify the effectiveness of theoretical results.

Minimum-energy synchronization control for interconnected networks is addressed, where network topologies contain leaderless and leader-follower structures and information transmission of the whole network is non-periodically silent. The key characteristic of the current work is that the total energy consumption is minimum in the sense of the linear matrix inequality, while both the guaranteed-cost synchronization and the limited-budget synchronization cannot make the total energy consumption be minimum. Firstly, the leaderless minimum-energy synchronization achievement problem is transformed into the asymptotic stabilization problem by the state decoupling strategy, and sufficient conditions of leaderless minimum-energy synchronization are presented by the Lyapunov-based method. Especially, those conditions can be solved by the generalized eigenvalue approach on the basis of the linear matrix inequality. Then, main results of leaderless minimum-energy synchronization are expanded to leader-follower interconnected networks, where the key challenge is that these networks are nonsymmetrical. Finally, two numerical examples are illustrated to verify main results.

Minimum-energy formation achievement problems for networked multiagent systems are investigated, where information networks with leaderless and leader-follower structures are respectively addressed and information networks are randomly switching. The critical feature of this work is that the energy constraint is minimum in the sense of the linear matrix inequality, but limited-budget control and guaranteed-cost control cannot realize a minimum-energy formation. Firstly, the leaderless minimum-energy formation control problem is converted into an asymptotic stability one via a nonsingular transformation and state space decomposition, and based on linear matrix inequality techniques, sufficient conditions for analysis and design of leaderless minimum-energy formation achievement are proposed, respectively, which can be solved by the generalized eigenvalue method. Then, main results of minimum-energy formation achievement of leaderless networked multiagent systems are extended leader-follower networked multiagent systems, where the asymmetric property of the leader-follower information network is well dealt with by two nonsingular transformations. Finally, two simulation examples are shown to verify the main results for minimum-energy formation achievements of leaderless and leader-follower networked multiagent systems, respectively.

The multi-AUV (Autonomous Underwater Vehicle) formation trajectory tracking control methods in the case of weak communication environment under discrete-time collection are studied in this paper. First, the discrete-time dynamic expression of the AUV model is given. Considering the environment disturbance, the communication structure with time-varying characteristics is divided into bounded and unbounded communication delay (packet losses) conditions. Then, the proposed coordinated trajectory tracking controller is discussed based on the leader-followers and the virtual leader method, and its convergence has been derived respectively. In addition, the switching topology communication structure caused by packet losses is discussed and analyzed. Finally, the simulation experiment verifies that the discrete-time multi-AUV system can form a fixed formation and achieve stable trajectory tracking under the bounded and unbounded communication delay in the underwater three-dimensional space.

This article addresses the three-dimensional (3-D) coordinated control problem of directed networked aircraft-like vehicles, that is to track a set of given orbits on a sphere and achieve a lateral formation flight. Different from the case of Newton particles, a nonholonomic dynamics with unknown disturbances is considered. A novel method to decouple the spherical orbit tracking subsystem and the lateral formation flying subsystem is proposed. By overlooking the control of the vehicle's surge velocity, a nonsmooth spherical orbit tracking algorithm is designed by backstepping. Without considering the spherical orbit tracking errors and using any global information of topologies, a distributed, nonsmooth formation protocol is designed. The input-to-state stability (ISS) theory is used to analyze the converge property of the interconnected system consisting of these two subsystems. Simulation results are given to verify the theoretical analysis.

The cooperative output tracking control problem of linear heterogeneous multi-agent systems with random communication constraints is investigated in this paper. An observer-based predictive control approach is proposed to actively compensate random communication constraints in the feedback channel of each agent and between agents. Moreover, the stability of closed-loop systems and output tracking performance are guaranteed. Finally, two simulation cases are carried out to verify the effectiveness of designed scheme.

This paper is concerned with the time-varying formation problem for second-order networked multi-agent systems, which are subject to random communication delays and packet dropouts in the sensor-to-controller and controller-to-actuator channels of each agent. A cloud-based time-varying formation predictive control method with control input quantization is proposed to actively compensate for those random communication constraints. A definition of quantized time-varying formation is given, and then a necessary and sufficient condition to achieve the quantized time-varying formation as well as the stability of the resulting closed-loop system is obtained, which is independent of random communication constraints and quantization errors. Simulation results are provided to verify the effectiveness of the proposed method.

Time-varying formation (TVF) and trajectory tracking
$H_{∞}$
control problem of multiagent systems (MASs) subject to communication delays and external disturbances under the directed communication topology is studied. This article's objective is for all agents to attain the desired TVF and track the pregiven formation center trajectory simultaneously. First, a distributed TVF and trajectory tracking control protocol employing neighborhood interaction information is developed in the presence of communication delays. Second, since the Laplacian matrix of a graph can be decomposed into the product of two specific matrices, the TVF and trajectory tracking
$H_{∞}$
control problem is converted into the lower dimension asymptotic stability problem of a closed-loop system by applying an appropriate variable conversion. Third, a Lyapunov-Krasovskii functional is constructed to analyze the stability of MASs. Sufficient conditions are obtained in the form of linear matrix inequalities (LMIs) to ensure the completion of the TVF and formation center trajectory tracking of MASs. In the meantime, the maximum allowable communication delay can be calculated by the LMIs. Finally, the results of numerical simulations are presented to verify the validity of the approach this article proposes.

This paper studies edge-based event-triggered strategies for the average consensus problem in multi-agent systems. To this end, a distributed event-triggered algorithm is presented based on edge information rather than neighbor information, where positive minimum inter-event times are guaranteed between all communication links in the network. Moreover, the triggering mechanism is constructed in a fully distributed way which uses only relative state differences based on local neighborhood information without any global graph topology information. This treatment greatly reduces the communication frequency compared with continuous-time average consensus algorithms. We show that the proposed algorithm makes all agents converge to the average of their initial states asymptotically, and the positive minimum inter-event time for each link is controllable by two corresponding agents through their triggering parameters.

Limited-energy output formation design and analysis problems are addressed for multiagent systems with intermittent interactions. Firstly, a new dynamic output feedback formation control protocol with the limited energy supply is proposed, which contains two independent parts associated with the interactive interval and the non-interactive interval. Then, sufficient conditions for leaderless limited-energy output formation are proposed by a new two-step design approach, which can make two gain matrices of the formation control protocol be designed independently. Meanwhile, the output formation reference function is determined to describe the absolute motion of all agents as a whole. Moreover, by constructing two transformation matrices with specific structures, the main conclusions for leaderless multiagent systems are extended into leader-follower ones. Finally, two numerical simulations are shown to demonstrate theoretical results.

This article investigates the dynamic consensus problem for the discrete-time second-order integrator networked multiagent system with time-varying delay and switching topology, in which the speed of each agent is not required to be synchronized to zero value. Novel consensus protocols using only relative state information are proposed, and sufficient conditions for dynamic consensus are derived. The results show that consensus can be reached for both the case with delay and the case without delay, if the gain is sufficiently small and the union of interaction graphs is scrambling or contains a spanning tree frequently enough as the system evolves. Numerical examples demonstrate the effectiveness of the theoretical results.

This article investigates admissible formation tracking for singular swarm systems under conditions of switching transmission topologies as well as the limited energy supply, where both switching transmission topologies containing a spanning tree and switching transmission topologies containing a joint spanning tree are addressed. First, a new formation control tracking protocol with switching transmission topologies is proposed to realize admissible formation tracking, where the total energy supply is predetermined. Afterwards, by a dual nonsingular transformation, the disagreement dynamics between followers and the leader is determined and the impacts of asymmetric structures of switching transmission topologies are eliminated. Sufficient conditions for admissible formation tracking design and analysis for singular swarm systems with switching transmission topologies containing a spanning tree and with switching transmission topologies containing a joint spanning tree are proposed, respectively, where the coupling relationship matrix between the total energy supply and the matrix variable is determined. Finally, two numerical simulations are presented to demonstrate the effectiveness of theoretical results.

This article considers the practical fixed-time self-triggered consensus tracking problem of delayed multiagent networks (MANs) subject to external disturbances under undirected topology and directed topology. The fixed-time consensus implies that the consensus is reached in a finite time and the convergence time is independent of initial conditions under the nonlinear consensus protocols. A self-triggered control (STC) strategy is developed based on the event-triggered control (ETC) strategy. For the ETC strategy, the nonlinear controllers and the measurement errors are designed based on the hyperbolic tangent function to avoid a nondifferential problem and Zeno behavior. To avoid continuous monitoring, the STC strategy is presented. Furthermore, the minimal interevent interval is strictly positive, which implies that no Zeno behavior occurs in the STC strategy. Finally, a numerical example is presented to verify the availability of the algorithms.

This paper studies the energy-constraint output formation control for swarm systems with leaderless and leader-following topology structures. Most existing results on output formation with the dynamic output feedback protocols focus on the swarm systems without the energy constraint, but it is well known that the energy constraint is critically important for practical applications. In order to analyze the impacts of the energy constraint, a new energy-constraint output formation protocol is proposed. First, by the observable decomposition approach, a dynamic output formation protocol is presented, which contains an energy-constraint term to restrict the whole consumption. Then, sufficient conditions for leaderless energy-constraint output formation are presented via establishing the relationship of the energy constraint and the matrix variables, where it is found that the designed gain matrices of the output formation protocol can ensure that the actual energy consumption is lower than the total energy supply. Especially, a partition checking algorithm is proposed to check those conditions, which can ensure the scalability and solvability of a swarm system. Moreover, the output formation center function is derived to depict the whole macroscopic movement of a swarm system. A nonsingular transformation approach is presented to unify leaderless energy-constraint output formation and energy-constraint output formation tracking into the same framework, which are usually discussed in different theoretical frameworks. Finally, two simulation examples are illustrated to show that the theoretical results about leaderless energy-constraint output formation and energy-constraint output formation tracking are correct.

In this paper, on-off SDRE control approach is presented for spacecraft formation flying control around sun-earth L2 libration point. Orbits around libration points are very good targets for many space missions mainly because of efficient fuel consumption. Furthermore, less propellant usage can be achieved by considering optimal control approaches in spacecraft formation flying control design. Among various nonlinear and optimal control methods, SDRE has shown to be a good controller in various missions due to the privileges including efficiency, accuracy and robustness. The spacecraft are assumed to have on-off thrusters as actuators. It requires them to be fed with a sequence of on-off pulses which is regarded as a challenge for spacecraft designers. Hence, the main contribution of this paper is designing an on-off SDRE approach for the formation flight around sun-earth L2 point with uncertainty with energy and accuracy considerations. Including on-off input as a constraint is not feasible for SDRE implementation because it makes the system non-affine. An alternative is utilizing an integral action technique and an auxiliary control to make the system affine which leads to on-off SDRE approach. It has also been shown that the proposed method is robust against parametric uncertainties of the states. Present study aims to design an energy-beneficial, simple and attractive controller for a complex nonlinear system with on-off inputs and uncertainty in CRTBP. Simulation results show that the on-off SDRE control could provide the formation flight around L2 point with high accuracy using less energy consumption.

This article considers the distributed output-feedback consensus control problem for nonlinear multiagent systems subject to input delays. Different from the existing related works, the input delay of each agent is described as an unknown time-varying function and is different from each other in this article. To deal with this problem, for each follower, we first construct a novel distributed observer based on the relative output information to asymptotically estimate the state information of the leader, then we introduce a classical observer to asymptotically estimate the state information of the follower based on its output information. By means of two observers, the leader-following consensus problem is transformed into the stability problem of the nonlinear system with unknown input delays. Subsequently, the distributed controller independent of delays is proposed for each follower by the use of the truncated prediction method under some conditions. Based on the Lyapunov stability theory, it is strictly proved that the distributed controller can render all agents achieving consensus. Finally, the effectiveness of the theoretical results is illustrated on the basis of numerical simulations on a group of single-link manipulators.

This article is concerned with the
$H_{\infty }$
cluster formation control of a multiagent system (MAS) with stochastic sampling in network environments. First, based on a directed communication topology with acyclic partition, agents are separated into several clusters. The agents moving in the same cluster are expected to achieve a desired formation collaboratively, while the agents in different clusters have different formation patterns. Second, the external disturbance for each agent is taken into account. The associated
$H_{\infty }$
cluster formation control, whose performance bound can be obtained by considering both formation information and cluster characteristics, is introduced to measure the disturbance attenuation ability. Third, by casting a stochastic sampled-data-based
$H_{\infty }$
cluster formation problem into an
$H_{\infty }$
control problem of a stochastic system, an
$H_{\infty }$
cluster formation criterion is derived for the MAS with external disturbance. Finally, a lower-dimensional cluster formation criterion is obtained for the disturbance-free MAS. Cluster formation performance analysis testifies the effectiveness of the proposed design methods.

Distributed cooperative encirclement hunting guidance strategy design and analysis issues for multiple flight vehicles system against a maneuvering target are considered in this paper. Distinct from the former results, the cooperative encirclement hunting guidance laws are based on the leader-follower coordination structure, and are divided into two parts. Firstly, for the leader flight vehicle, a full-head-on interception guidance law is proposed against the maneuvering target, where the uncertain dynamics and the target's unknown maneuver are estimated and compensated by using an extended state observer. For the follower flight vehicles, the distributed time-varying encirclement hunting line of sight angle formation tracking laws with overload saturation are designed where distributed extended state observers are introduced to approximate the complicated uncertain items and the leader vehicle's input signals. Then, the design processes of cooperative encirclement hunting guidance laws are summarized within five steps as an algorithm. Thirdly, the stability and the properties of the proposed cooperative encirclement hunting guidance algorithm are analyzed by employing Lyapunov theories. Finally, numerical simulation results illustrate the effectiveness of achieved cooperative encirclement hunting guidance strategies.

Controllers learned from data are more practical and promising than the existing model-based ones and their capability can be enhanced if a priori information about the controlled plant is available. Under this viewpoint, a data-driven guaranteed cost control (GCC) design is investigated for linear systems with time-varying parameter uncertainties. Initially, the GCC design is shown to be equivalent to an H
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state feedback control problem subject to a specific disturbance attenuation performance requirement. Then such an H
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control problem is regarded as a zero-sum game and reduces to seek the stabilizing solution of a parameterized algebraic Riccati equation (ARE). Furthermore, to solve the ARE approximately, a modified simultaneous policy update algorithm (SPUA) and the corresponding data-driven variant based on off-policy reinforcement learning (RL) and experience replay technique is proposed. Finally, a numerical simulation for aircrafts with harsh uncertainties is illustrated to validate the merits of the proposed methods.

Practical time-varying output formation tracking problems with collision avoidance, obstacle dodging and connectivity maintenance for high-order multi-agent systems are investigated, and the practical time-varying output formation tracking error is controlled within an arbitrarily small bound. The outputs of followers are designed to track the output of the leader with unknown control input while retaining the predefined time-varying formation. Uncertainties are considered in the dynamics of the followers and the leader. Firstly, distributed extended state observers are developed to estimate the uncertainties and the leader’s unknown control input. A strategy of obstacle dodging is given by designing an ideal secure position for the followers which are in the threatened area of the obstacles. By constructing collision avoidance, obstacle dodging and connectivity maintenance artificial potential functions, corresponding negative gradient terms are calculated to achieve the safety guarantee. Secondly, a practical time-varying output formation tracking protocol is proposed by using distributed extended state observers and the negative gradient terms. Additionally, an approach is presented to determine the gain parameters in the protocol. The stability of the closed-loop multi-agent system with the protocol is analyzed by using Lyapunov stability theory. Finally, a simulation experiment is provided to illustrate the effectiveness of the obtained methods.

This paper addresses the formation control problem for a group of mechanical systems with nonlinear uncertain dynamics under the virtual leader-following framework. New cooperative deterministic learning-based adaptive formation control algorithms are proposed. Specifically, the virtual leader dynamics is constructed as a linear system subject to bounded inputs, so as to produce more diverse reference signals for formation tracking control. A cooperative discontinuous nonlinear estimation protocol is first proposed to estimate the leader's state information. Based on this, a cooperative deterministic learning formation control protocol is developed using artificial neural networks, such that formation tracking control and locally-accurate nonlinear identification with learning knowledge consensus can be achieved simultaneously. Finally, by utilizing the learned knowledge represented by constant neural networks, an experience-based distributed control protocol is further proposed to enable position-swappable formation control. Numerical simulations using a group of autonomous underwater vehicles have been conducted to demonstrate the effectiveness and usefulness of the proposed results.

This paper addresses the problem of leader-following consensus control of general linear multi-agent systems (MASs) with diverse time-varying input delays under the integral quadratic constraint (IQC) framework. A novel exact-memory distributed output-feedback delay controller structure is proposed, which utilizes not only relative estimation state information from neighboring agents but also local real-time information of time delays and the associated dynamic IQC-induced states from the agent itself for feedback control. As a result, the distributed consensus problem can be decomposed into H∞ stabilization subproblems for a set of independent linear fractional transformation (LFT) systems, whose dimensions are equal to that of a single agent plant plus the associated local IQC dynamics. New delay control synthesis conditions for each subproblem are fully characterized as linear matrix inequalities (LMIs). A numerical example is used to demonstrate the proposed approach.

In this study, the cooperative output regulation problem for heterogeneous multi-agent systems is addressed by considering a leader dynamics subject to bounded (possibly non-zero, persistent, and time varying) inputs. Compared to many existing works with a leader of zero input, using such a leader dynamics will facilitate realisation of more diverse and sophisticated tracking trajectories for cooperative output regulation control. However, it also poses a challenge to pursue exact output regulation performance. To this end, a new two-layer hierarchical design framework is proposed. This framework consists of an upper-layer cooperative estimator for estimating the leader's state information in finite time, and a lower-layer distributed output regulator to achieve exact output regulation performance. Both finite-time estimation and asymptotic output regulation performance are analysed using the Lyapunov function method, and the associated solvability conditions are established as a set of linear matrix inequalities plus linear matrix equations. Simulation studies are also included to demonstrate the effectiveness of the proposed approach.

This paper proposes a distributed model free adaptive iterative learning control (MFAILC) method for a class of unknown nonlinear multiagent systems to perform consensus tracking. Here, both fixed and iteration-varying topologies are considered and only a subset of followers can access the desired trajectory in each topology. To design the control protocol, the agent's dynamic is first transformed into a dynamic linearization model along the iteration axis, and then a distributed MFAILC scheme is constructed to guarantee that all agents can track the desired trajectory. Through rigorous analysis, it is shown that under this novel distributed MFAILC scheme, the tracking errors of all agents are convergent along the iteration axis. The main merit of this design is that consensus tracking task can be achieved only utilizing the input/output data of the multiagent system. Three examples are given to validate the effectiveness of the proposed design.

This paper considers the leader-follower tracking control problem for linear
interconnected systems with undirected topology and linear dynamic coupling.
Interactions between the systems are treated as linear dynamic uncertainty and
are described in terms of integral quadratic constraints (IQCs). A
consensus-type tracking control protocol is proposed for each system based on
its state relative its neighbors. In addition a selected set of subsystems uses
for control their relative states with respect to the leader. Two methods are
proposed for the design of this control protocol. One method uses a coordinate
transformation to recast the protocol design problem as a decentralized robust
control problem for an auxiliary interconnected large scale system. Another
method is direct, it does not employ coordinate transformation; it also allows
for more general linear uncertain interactions. Using these methods, sufficient
conditions are obtained which guarantee that the system tracks the leader.
These conditions guarantee a suboptimal bound on the system consensus and
tracking performance. The proposed methods are compared using a simulation
example, and their effectiveness is discussed. Also, algorithms are proposed
for computing suboptimal controllers.

The aim of this paper is to present rigorous and efficient methods for designing flight controllers for unmanned helicopters that have guaranteed performance, intuitive appeal for the flight control engineer, and prescribed multivariableloopstructures.Helicopterdynamicsdonotdecoupleastheydoforthe fixed-wingaircraftcase,andso the design of helicopter flight controllers with a desirable and intuitive structure is not straightforward. We use an H1 output-feedback design procedure thatis simplified in the sense that rigorous controller designs are obtained by solving only two coupled-matrix design equations. An efficient algorithm is given for solving these that does not require initial stabilizing gains. An output-feedback approach is given that allows one to selectively close prescribed multivariable feedbackloopsusing areducedsetof thestates ateach step.At eachstep,shaping filtersmay beadded thatimproveperformanceandyieldguaranteedrobustnessandspeedofresponse.ThenetresultyieldsanH1 design with a control structure that has been historically accepted in the flight control community. As an example, a design forstationkeepingandhoverofanunmannedhelicopterispresented.Theresult isastationkeeping hovercontroller withrobustperformanceinthepresenceofdisturbances(includingwindgusts),excellentdecoupling,andgoodspeed of response.

Graphs.- Groups.- Transitive Graphs.- Arc-Transitive Graphs.- Generalized Polygons and Moore Graphs.- Homomorphisms.- Kneser Graphs.- Matrix Theory.- Interlacing.- Strongly Regular Graphs.- Two-Graphs.- Line Graphs and Eigenvalues.- The Laplacian of a Graph.- Cuts and Flows.- The Rank Polynomial.- Knots.- Knots and Eulerian Cycles.- Glossary of Symbols.- Index.

For linear-quadratic dynamic games in which norm-bounded time-varying uncertainty enters in all matrices of the system equation without assuming the matching conditions, the notions of robust minimax and maximin strategies are introduced. It is shown how to construct two auxiliary dynamic games with completely known equations in such a way that a minimax strategy for one of them and a maximin strategy for the other turn out to be the robust minimax and maximin strategies, respectively, for the original dynamic game. By assuming 'control' as the first player and 'disturbance' as the second player, we show that the robust minimax strategy in the appropriate dynamic game provides the uncertain system with a robust H infinity suboptimal control, which guarantees quadratic stability of the unforced uncertain system. The results presented in this paper generalize those obtained in previous works.

A novel nonlinear sliding mode control approach dealing with the formation control of under-actuated ships is presented in this paper. To avoid the singularity problem, state space of the system is partitioned into two regions, with one region bounded for terminal sliding mode control and its complement singular for that. And a linear auxiliary sliding mode controller is designed for system trajectories starting from the complement region. With the application of nonlinear sliding mode control approach and finite-time stability theory, a distributed controller is designed for individual under-actuated ship to achieve the given formation pattern within a finite time. Finally, two simulation examples are provided to verify the effectiveness and performance of the proposed approach.

This paper addresses the mean square consensus problem of leader-following stochastic multi-agent systems using a distributed event-triggered control strategy. For each involving agent, generally, the time-varying (or fixed) delay between controller and actuator is unavoidable. The controller is updated only when the event condition is triggered. Based on the Lyapunov function method and Itô formula, three sufficient conditions for leader-following mean square consensus are established, including a delay-independent consensus condition and a delay-dependent criterion for the case with input fixed time delay, and a consensus criterion for the case with input time-varying delay. Furthermore, an inter-event time lower bound between two sampling points is derived. The results are illustrated through several numerical examples.

In this paper, the problem of distributed event-triggered pinning control for practical consensus of multiagent systems (MASs) with quantized communication based on a directed graph is investigated. The pinning control for practical consensus of MASs with uniform quantizer is first discussed. Then, in order to decrease communication load of interagent, the event-triggered quantized communication protocol is designed. The nonsmooth analysis and Gronwall's inequality approach is used to guarantee the existence of a solution to the resulting closed-loop system. It is shown that practical consensus is reachable through the event-triggered control and converges to a consensus set. Moreover, "Zeno phenomenon" can be excluded. Finally, an example is given to validate the feasibility and efficiency of the proposed new design method.

This paper is concerned with the output-feedback controller design for consensus of a class of heterogeneous linear multi-agent systems with the aperiodic sampled-data industrial measurement. Under mild assumptions that the sampling periods are taken from a given set and the agent systems are timesynchronized, an equivalent switched system model is first proposed for the heterogeneous agent system with nonuniform sampling. The overall leader-following tracking control problem (LFTCP) is then formulated as the output regulation of a discretetime switched system. By using some algebraic manipulations, the control problem under consideration is further decoupled into two control sub-problems, i.e., a static output-feedback control problem plus a simple feedback control problem related to the communication topology. Based on the Lyapunov stability theory, some sufficient conditions are obtained for the solvability of LFTCP. In our results, the static output-feedback controller gains are determined by solving some strict linear matrix inequalities. Finally, a simulation study on the modified Caltech multi-vehicle wireless testbed is presented to show the effectiveness of the proposed design method.

The research of this paper works out the attitude and position control of the flapping wing micro aerial vehicle (FWMAV). Neural network control with full state and output feedback are designed to deal with uncertainties in this complex nonlinear FWMAV dynamic system and enhance the system robustness. Meanwhile, we design disturbance observers which are exerted into the FWMAV system via feedforward loops to counteract the bad influence of disturbances. Then, a Lyapunov function is proposed to prove the closed-loop system stability and the semi-global uniform ultimate boundedness of all state variables. Finally, a series of simulation results indicate that proposed controllers can track desired trajectories well via selecting appropriate control gains. And the designed controllers possess potential applications in FWMAVs.

Intelligent techniques foster the dissemination of new discoveries and novel technologies that advance the ability of robots to assist and support humans. The human-centered intelligent robot has become an important research field that spans all of the robot capabilities including navigation, intelligent control, pattern recognition and human-robot interaction. This paper focuses on the recent achievements and presents a survey of existing works on human-centered robots. Furthermore, we provide a comprehensive survey of the recent development of the human-centered intelligent robot and discuss the issues and challenges in the field.

In this paper, the leader-following consensus problem of high-order multiagent systems via event-triggered control is discussed. A novel distributed event-triggered communication protocol based on state estimates of neighboring agents is proposed to solve the consensus problem of the leader-following systems. We first investigate the consensus problem in a fixed topology, and then extend to the switching topologies. State estimates in fixed topology are only updated when the trigger condition is satisfied. However, state estimates in switching topologies are renewed with two cases: 1) the communication topology is switched or 2) the trigger condition is satisfied. Clearly, compared to continuous-time interaction, this protocol can greatly reduce the communication load of multiagent networks. Besides, the event-triggering function is constructed based on the local information and a new event-triggered rule is given. Moreover, "Zeno behavior" can be excluded. Finally, we give two examples to validate the feasibility and efficiency of our approach.

In this paper, we present a novel approach for tracking control with switching formation in nonomniscient constrained space for multiagent system (MAS). The introduction of switching formation results from the situation where MAS is maneuvering in restricted path which is often the case for real world application. The preplanned trajectory may be inaccurate due to the lack of sufficient environmental information. In this case, agents may have to rapidly avoid collisions with unexpected obstacles or even switch the formation to guarantee the passability. A concept of avoidless disturbance is proposed. To solve the undesirable chattering on resulting trajectory caused by avoidless disturbance and the existing adaptation algorithm for neural network (NN) weights, a local path replanning approach is designed such that the potential force generated by avoidless disturbance is acted on the original desired trajectory outputting the locally replanned path for an agent. An NN-based controller is designed and the performance is validated using Lyapunov functions. Simulations are carried out to illustrate the effectiveness of proposed strategies.

Leader-following guaranteed-performance consensus problems for singular multi-agent systems with Lipschitz nonlinear dynamics are investigated. To obtain leader-following guaranteed-performance consensus, the consensus protocol and quadratic performance function based on state errors are proposed. Then, leader-following consensus problems of a nonlinear singular multi-agent system are transformed into asymptotic stabilization problems of a reduced-order subsystem by a new state decomposition method, and the impacts of the Lipschitz nonlinear dynamics are eliminated by using the structure property of the transformation matrix and the Lipschitz condition. Moreover, a guaranteed-performance consensualization criterion based on the Riccati inequality is given and the guaranteed-performance cost with a new structure is determined. Finally, a numerical simulation is shown to verify the validity of theoretical results.

This paper deals with the tracking control problem for a class of nonlinear multiple input multiple output unknown time-varying delay systems with full state constraints. To overcome the challenges which cause by the appearances of the unknown time-varying delays and full-state constraints simultaneously in the systems, an adaptive control method is presented for such systems for the first time. The appropriate Lyapunov-Krasovskii functions and a separation technique are employed to eliminate the effect of unknown time-varying delays. The barrier Lyapunov functions are employed to prevent the violation of the full state constraints. The singular problems are dealt with by introducing the signal function. Finally, it is proven that the proposed method can both guarantee the good tracking performance of the systems output, all states are remained in the constrained interval and all the closed-loop signals are bounded in the design process based on choosing appropriate design parameters. The practicability of the proposed control technique is demonstrated by a simulation study in this paper.

This paper investigates the data-driven consensus tracking problem for multiagent systems with both fixed communication topology and switching topology by utilizing a distributed model free adaptive control (MFAC) method. Here, agent's dynamics are described by unknown nonlinear systems and only a subset of followers can access the desired trajectory. The dynamical linearization technique is applied to each agent based on the pseudo partial derivative, and then, a distributed MFAC algorithm is proposed to ensure that all agents can track the desired trajectory. It is shown that the consensus error can be reduced for both time invariable and time varying desired trajectories. The main feature of this design is that consensus tracking can be achieved using only input-output data of each agent. The effectiveness of the proposed design is verified by simulation examples.

This paper is concerned with the leader-follower consensus of multiagent systems with wireless communications with the main objective of reducing the power consumption. First, by assuming that the sampling period jumps from one to another only from a given set, a new stochastic sampling approach is introduced to reduce the sampling frequency of each agent. Then, only 1-D of the sampled data is selected, and transmitted to its neighboring agents. Finally, each agent is scheduled to communicate with others intermittently. A unified Markovian system model is proposed to capture the above stochastic sampling, measurement selection scheme and intermittent transmission process, and such a novel protocol can significantly reduce the power consumption. Based on the Lyapunov stability theory and the Markovian jump system approach, the distributed consensus-based controller gain is obtained by solving an optimization problem. The advantage of the proposed consensus protocol is verified by two simulation examples. The simulation results explicitly show our result is more energy-efficient than that of existing one.

Time-varying formation tracking problems for linear multi-agent systems with multiple leaders are studied, where the states of followers form a predefined time-varying formation while tracking the convex combination of the states of multiple leaders. Followers are classified into well-informed ones and uninformed ones, where the neighbor set of the former contains all the leaders while the latter contains no leaders. A formation tracking protocol is constructed using only neighboring relative information. Necessary and sufficient conditions for multi-agent systems with multiple leaders to achieve time-varying formation tracking are proposed by utilizing the properties of the Laplacian matrix, where the formation tracking feasibility constraints are also given. An approach to design the formation tracking protocol is presented by solving an algebraic Riccati equation. The obtained results can be applied to deal with time-varying formation tracking problems, target enclosing problems and consensus tracking problems for linear multi-agent systems with one or multiple targets/leaders. Numerical simulations are provided to demonstrate the effectiveness of the theoretical results.

By employing the finite-time control method, the consensus control algorithm for higher-order multiagent systems is designed in this paper. Under a neighbor-based rule, a higher-order finite-time consensus algorithm is explicitly constructed, which only uses local information. The finite-time consensus control algorithm can guarantee that the state consensus is achieved in a finite time. In addition, for multiagent systems having a leader-following structure, the consensus algorithm is also designed. Finally, two examples are presented to show the effectiveness.

Different from traditional centralized control, one major challenge of distributed consensus tracking control lies in the constraint that the desired reference trajectory is only accessible by part of the subsystems. Currently, most existing schemes require the availability of partial knowledge of the reference trajectories to all of the subsystems or information exchange of local control inputs. In this paper, we investigate distributed adaptive consensus tracking control without such requirements for nonlinear high-order multi-agent systems subjected to mismatched unknown parameters and uncertain external disturbances. By introducing compensating terms in a smooth function form of consensus errors and certain positive integrable functions in each step of virtual control design, a new backstepping based distributed adaptive control protocol is proposed. An extra estimator is designed in each subsystem to handle the parametric uncertainties involved in its neighbors’ dynamics, which avoids information exchange of local neighborhood consensus errors among connected subsystems. It is shown that global uniform boundedness of all the closed-loop signals and asymptotically output consensus tracking can be achieved. Simulation results are provided to verify the effectiveness of our scheme.

This paper is concerned with the optimal guaranteed cost sliding-mode control problem for interval type-2 (IT2) Takagi-Sugeno fuzzy systems with time-varying delays and exogenous disturbances. In the presence of the uncertain parameters hidden in membership functions, an adaptive method is presented to handle the time-varying weight coefficients reflecting the change of the uncertain parameters. A new integral sliding surface is presented based on the system output. By designing a novel adaptive sliding-mode controller, system perturbation or modeling error can be compensated, and the reachability of the sliding surface can be guaranteed with the ultimate uniform boundedness of the closed-loop system. Optimal conditions of an H
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guaranteed cost function and an H
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performance index are established for the resulting time-delay control system. Finally, an inverted pendulum system represented by the IT2 fuzzy model is applied to illustrate the advantages and effectiveness of the proposed control scheme.

To investigate the energy consumption involved in a sampled-data consensus process, the problem of guaranteed cost consensus for sampled-data linear multi-agent systems is considered. By using an input delay approach, an equivalent system is constructed to convert the guaranteed cost consensus problem to a guaranteed cost stabilization problem. A sufficient condition for guaranteed cost consensus is given in terms of linear matrix inequalities (LMIs), based on a refined time-dependent Lyapunov functional analysis. Reduced-order protocol design methodologies are proposed, with further discussions on determining sub-optimal protocol gain and enlarging allowable sampling interval bound made as a complement. Simulation results illustrate the effectiveness of the theoretical results.

The robust guaranteed cost consensus problem of high-order discrete-time linear multi-agent systems (MASs) with parameter uncertainties and time-varying delays is studied, and a linear consensus protocol of it is designed. Norm-bounded uncertainties and polytopic uncertainties are considered. First, the idea of robust guaranteed cost control is introduced into consensus problems for the MASs, where a cost function is defined based on state errors among neighbouring agents and control inputs of all the agents. Second, by constructing suitable Lyapunov functions and using the stability theory of discretetime linear systems, two sufficient linear matrix inequality conditions are derived to insure that high-order discrete-time linear MASs with the two types of parameter uncertainties and time-varying delays reach robust guaranteed cost consensus. At the same time, two upper bounds of the guaranteed cost function are also given. Third, convergence results are given as final consensus values of the MASs with parameter uncertainties and time-varying delays. Finally, two numerical comparisons are given to illustrate the correctness and availability of the theoretical results.

Time-varying formation tracking analysis and design problems for second-order Multi-Agent systems with switching interaction topologies are studied, where the states of the followers form a predefined time-varying formation while tracking the state of the leader. A formation tracking protocol is constructed based on the relative information of the neighboring agents. Necessary and sufficient conditions for Multi-Agent systems with switching interaction topologies to achieve time-varying formation tracking are proposed together with the formation tracking feasibility constraint based on the graph theory. An approach to design the formation tracking protocol is proposed by solving an algebraic Riccati equation, and the stability of the proposed approach is proved using the common Lyapunov stability theory. The obtained results are applied to solve the target enclosing problem of a multiquadrotor unmanned aerial vehicle (UAV) system consisting of one leader (target) quadrotor UAV and three follower quadrotor UAVs. A numerical simulation and an outdoor experiment are presented to demonstrate the effectiveness of the theoretical results.

In this brief, the control problem for flexible wings of a robotic aircraft is addressed by using boundary control schemes. Inspired by birds and bats, the wing with flexibility and articulation is modeled as a distributed parameter system described by hybrid partial differential equations and ordinary differential equations. Boundary control for both wing twist and bending is proposed on the original coupled dynamics, and bounded stability is proved by introducing a proper Lyapunov function. The effectiveness of the proposed control is verified by simulations.

This paper considers the time-varying formation problem of tracking a reference for a class of networked systems consisting of multiple nonlinear subsystems with unknown parameters and non-identical nonlinear dynamics. The communication status among the subsystems is represented by a directed graph. A portion of subsystems have no access to the information of reference. Distributed adaptive controllers are proposed by employing backstepping technique. It is proved that, with the proposed scheme, all the closed-loop signals are globally bounded and all the subsystems can track the reference while building and keeping the prescribed time-varying formation shape. Simulation results are given to illustrate the effectiveness of the proposed scheme.

This paper is concerned with the consensus tracking control problem for linear leader-follower systems with switching directed networks and exogenous disturbances, where the condition of zero control input for leader node is not assumed. Suppose the interaction network of all subsystems may switch among finite digraphs, which contains some non-identical directed spanning trees. Based only on the state information of neighboring agents, a design procedure for constructing the distributed consensus protocol is developed. By employing the topology-dependent multiple Lyapunov functions (MLFs) method and algebraic graph theory, the criteria of consensus protocol design is given in terms of linear matrix inequalities (LMIs). It is proved that the consensus tracking problem for multi-agent systems (MASs) under dynamic directed topologies can be solvable if the topology average dwell time satisfies a certain switching condition. Finally, a network system of F-18 aircraft is given as an example to verify the effectiveness of the proposed design method.

This paper considers a leader-follower formation control problem of nonholonomic vehicles of unicycle-type subject to velocity constraints. The velocity constraints of each vehicle are described by saturated angular velocity and bounded linear velocity lying between two positive constants. The communication topology of the networked multi-vehicle system is modeled by a directed graph. The designed control law is distributed in the sense that the controller of each follower vehicle only uses its own information and the information of its neighboring vehicles. It is shown that with the proposed control law, the leader-follower formation can be achieved without using absolute position measurements while the velocity constraints are satisfied. Finally, the simulation results of an example verify effectiveness of the proposed control law.

This paper is concerned with the consensus problem for multi-agent systems with switching topology. A novel distributed control strategy is proposed to reduce the frequency of controller update and save network resources. Based on communication uncertainty of practical networks, partial information exchange and switching topology which subjects to a heterogeneous Markov chain are considered in controller design. An H∞ consensus criterion is derived by using linear matrix inequality and Lyapunov methods. According to this consensus criterion, a sufficient condition on designing H∞ state-feedback controller is presented. Finally, a simulation example is given to illustrate the effectiveness of the proposed event-based control strategy.

In this paper, formation tracking control based on potential field is studied. The objective is to control a group of agents to track a desired trajectory while maintaining a given formation in nonomniscient constrained space. Aiming at this purpose, the average of all agents' positions is viewed as the virtual leader, and the task is translated into that controlling the virtual leader to track the center of the desired formation. The situation where agents may not have global environmental information will lead to that they may have to avoid collisions with unexpected spatial constraints. By introducing the concepts of line source and surface source, two main types of spatial constraints: 1) borders and 2) obstacles are defined mathematically and unified into a common expression in an artificial potential function. In this way, the tasks of formation tracking and obstacle avoidance in a bounded environment can be solved by the control law proposed in this paper. Furthermore, concerning the situation of multiple spatial constraints, a Dirac delta function is introduced. Meanwhile, a formation optimal algorithm is proposed to minimize the formation generation time cost. Following that, a controller is designed, and the conditions for asymptotic stability of multiagent systems are proved based on the Lyapunov function. The maximum duration that the conditions cannot be satisfied is elaborated to indicate whether the tracking task should be given up. Meanwhile, the impulsive influence from spatial constraints is analyzed. Finally, the simulation results are presented to illustrate the performance of proposed approaches.

Containment analysis and design problems for general high-order linear time-invariant multi-agent systems with time-varying delays are studied, where the interaction topology is directed. Using the state information of each agent and neighboring agents, a protocol with time-varying delays is constructed, where the motion modes of the leaders can be specified. Based on Lyapunov–Krasovskii stability theory, sufficient conditions for general linear multi-agent systems with time-varying delays to achieve containment are proposed which only include four linear matrix inequalities independent of the number of agents. Moreover, an approach to determine the gain matrices in the protocol is presented. Finally, a numerical example is given to demonstrate the effectiveness of the obtained theoretical results.

In this technical note, the H
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consensus control problem is investigated over a finite horizon for general discrete time-varying multi-agent systems subject to energy-bounded external disturbances. A decentralized estimation-based output feedback control protocol is put forward via the relative output measurements. A novel event-based mechanism is proposed for each intelligent agent to utilize the available information in order to decide when to broadcast messages and update control input. The aim of the problem addressed is to co-design the time-varying controller and estimator parameters such that the controlled multi-agent systems achieve consensus with a disturbance attenuation level γ over a finite horizon [0, T]. A constrained recursive Riccati difference equation approach is developed to derive the sufficient conditions under which the H
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consensus performance is guaranteed in the framework of event-based scheme. Furthermore, the desired controller and estimator parameters can be iteratively computed by resorting to the Moore-Penrose pseudo inverse. Finally, the effectiveness of the developed event-based H∞ consensus control strategy is demonstrated in the numerical simulation.

This paper investigates the distributed consensus tracking problems of multi-agent systems on undirected graph with a fixed topology. Each follower is assumed to be in strict-feedback form with unknown state-dependent controlling effects. A distributed robust adaptive neural networks-based control scheme is designed to guarantee the consensus output tracking errors between the followers and the leader are cooperatively semi-globally uniformly ultimately bounded. Command filtered backstepping technique is extended to the consensus tracking control problems, which avoids the classical “explosion of complexity” problem in standard backstepping design and removes the assumption that the first derivatives of the leader’s output should be known. The function approximation technique using neural networks is employed to compensate for unknown functions induced from the controller design procedure. Stability analysis and parameter convergence of the proposed algorithm are conducted based on algebraic graph theory and Lyapunov theory.

This paper addresses some fundamental issues in adaptive control of aircraft with structural damage. It presents a thorough study of linearized aircraft models with damage to obtain new details of system descriptions, such as coupling and partial derivatives of lateral and longitudinal dynamics. A detailed study of system invariance under damage conditions is performed for generic aircraft models to obtain key system characterizations for model reference adaptive control, such as infinite zero structure and signs of high-frequency gain matrices. A comprehensive study of multivariable model reference adaptive control systems in the presence of damage is performed to obtain critical design specifications for adaptive flight control, such as system and controller parameterizations and adaptive parameter update laws. Both analytical and simulation results are given to illustrate the design and performance of adaptive control systems for aircraft flight control.

This paper is devoted to the output consensus problem of directed networks of multiple high-order agents with external disturbances, and proposes a distributed protocol using the neighbors' measured outputs. By defining an appropriate controlled output and conducting a model transformation in two steps, consensus performance analysis of the multi-agent system under the proposed protocol is transformed into a normal H∞ problem. Then using H∞ theory of linear systems, conditions are derived to ensure the consensus performance with a prescribed H∞ index for networks with fixed and switching topologies, respectively. A numerical example of the formation control application is included to validate the theoretical results. Copyright © 2009 John Wiley & Sons, Ltd.

Formation flying is an emerging area in the Earth and space science and technology domains that utilize multiple inexpensive spacecraft by distributing the functionalities of a single platform spacecraft among miniature inexpensive platforms. Traditional spacecraft fault diagnosis and health monitoring practices involve around-the-clock monitoring, threshold checking, and trend analysis of a large amount of telemetry data by human experts that do not scale well for multiple space platforms. A novel hierarchical fault diagnosis framework and methodology is presented here that enables a systematic utilization of fuzzy rule-based reasoning to enhance the level of autonomy achievable in fault diagnosis at ground stations. Fuzzy rule-based fault diagnosis schemes for satellite formation flight are developed and investigated at different levels in the hierarchy for a leader-follower architecture. Our formation level fault diagnosis is found to be useful as a supervisory diagnosis scheme that can prompt the operators to have a closer look at the potential faulty components to determine the sources of a fault. Effectiveness of our proposed fault diagnosis methodology is demonstrated by utilizing synthetic formation flying data of five satellites that are configured in the leader-follower architecture, and are subjected to nonabrupt intermittent faults in the attitude control subsystem (ACS) and the electrical power subsystem (EPS) of the follower satellites.

In this paper, we study the consensus problem in multi-vehicle systems, where the information states of all vehicles approach a time-varying reference state under the condition that only a portion of the vehicles (e.g., the unique team leader) have access to the reference state and the portion of the vehicles might not have a directed path to all of the other vehicles in the team. We first analyze a consensus algorithm with a constant reference state using graph theoretical tools. We then propose consensus algorithms with a time-varying reference state and show necessary and sufficient conditions under which consensus is reached on the time-varying reference state. The time-varying reference state can be an exogenous signal or evolve according to a nonlinear model. These consensus algorithms are also extended to achieve relative state deviations among the vehicles. An application example to multi-vehicle formation control is given as a proof of concept.

Guaranteed cost consensus for multi-agent systems with switching topologies

- Z Wang
- J X Xi
- Z C Yao
- G B Liu