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Distributed L2-gain output-feedback control of homogeneous and heterogeneous systems
Abstract
The importance of static output feedback (OPFB) design for aircraft control, process control, and elsewhere has been well documented since the 1960s, since full state measurements are not usually available in practical systems. This problem is compounded in the case of multi-agent systems (MAS) where each agent has its own state variable and measured outputs. Therefore, this paper addresses the Ⅎ2-gain OPFB synchronization of linear MAS subject to external disturbances. Both homogeneous and heterogeneous MAS are considered. For homogeneous MAS, it is shown that the Ⅎ2-gain static OPFB synchronization problem of MAS can be cast into the Ⅎ2-gain static OPFB problem for a set of decoupled systems that depend on the graph topology. A modified Riccati equation is introduced which gives the OPFB gain and the coupling gain of the proposed static OPFB control protocol. For heterogeneous MAS, it is shown that the Ⅎ2-gain synchronization problem can be cast into the Ⅎ2-gain static OPFB problem of a set of decoupled systems plus a coupling condition on their dynamic compensators that depends on the graph topology. A certain novel gain matrix is introduced in the dynamics of the control protocol to improve the performance.
... Within the boundary of this setup different approaches have yielded various interesting solutions to the synchronization problem, where the universal goal is to drive the agents' states x i (t) to a common trajectory. E.g., communication delays are considered in [15], L 2 -gain output-feedback is employed in [2], distributed containment problem is studied in [4]. Among many other works contributing to our wealth of knowledge are [5] on adaptive protocols, [8] on switching topologies, and [14] on optimal state feedback and observer design. ...
... 1 and n (2) 1 , the current source u 12 connects n (1) p and n (2) p . Since for these two current sources the indices (1 and p) of the nodes they are associated to are different, we cannot find a scalar a that satisfies B 12 = aB 32 . ...
... 1 and n (2) 1 , the current source u 12 connects n (1) p and n (2) p . Since for these two current sources the indices (1 and p) of the nodes they are associated to are different, we cannot find a scalar a that satisfies B 12 = aB 32 . ...
Synchronization in networks of discrete-time linear time-invariant systems is considered under relative actuation. Neither input nor output matrices are assumed to be commensurable. A distributed algorithm that ensures synchronization via dynamic relative output feedback is presented.
... We study a general Dynamic Output Feedback(DOF) structure. For single-agent systems, it has been studied, among others, by in [5]- [8] and Masubuchi in [9]. In the latter, in particular, a variety of objectives, from stability to l 2 gain and other performance objectives, have been addressed, both in continuous and discrete times. ...
... for zero initial conditions, x cl (k) stays inside the ellipsoid E ξ2 = x cl : x T cl P x cl ≤ ξ 2 2 , and the Σ sat cl l2 < γ. Proof: Consider the P, T as in (8). Pre-and-post multiply (16) by diag P T −1 , I m and its transpose: ...
... Without loss of generality, we arrange 0 < λ = λ 1 ≤ λ 2 ≤ · · · ≤ λ N =λ. ConsiderP = I N ⊗ P,T = U ⊗ T in Lemma 2 where P, T are taken as in (8). Pre-and-post multipling (5) by diag TP −1 , I m+r ,T , I q and its transpose leads to: ...
... To solve consensus problems in the heterogeneous framework, where agents are modeled as linear systems, different protocols have been recently proposed, ranging from the H ∞ for ensuring robust leadertracking performances in the presence of external perturbation [1,15,22,63], to adaptive approaches such as the ones proposed in [5,57] for tackling the leaderfollower control problem, or in [19,20,31] for solving containment and formation problems. ...
... In this context, the presence of the leading behavior is usually modeled as an autonomous agent (leader) generating the reference trajectories, belonging to a prescribed family that have to be tracked by all agents (followers). For the case of heterogeneous, but linear, MASs, it is possible to prove that this goal can be reached if a set of linear matrix equations, defined as regulator equations, are verified for each agent (e.g., see [22] and references therein). To this aim, most of the approaches in the technical literature propose joining the solutions of the regulator equations to the design of distributed observers in order to estimate the leader behavior (or a convex combination of the leaders states in the multi-leader case) [22,45]. ...
... For the case of heterogeneous, but linear, MASs, it is possible to prove that this goal can be reached if a set of linear matrix equations, defined as regulator equations, are verified for each agent (e.g., see [22] and references therein). To this aim, most of the approaches in the technical literature propose joining the solutions of the regulator equations to the design of distributed observers in order to estimate the leader behavior (or a convex combination of the leaders states in the multi-leader case) [22,45]. However, this estimation funds on the precise knowledge of the leader matrix [64]. ...
This paper addresses the leader tracking control problem for heterogeneous uncertain nonlinear multi-agent systems sharing information via a communication network, modeled as a directed graph. To solve the problem, we propose a novel distributed PID-like control strategy which, enhanced with a Lyapunov-based adaption mechanism for the control parameters, is able to counteract the uncertainties acting on the agents dynamics. The stability analysis analytically proves the effectiveness of the proposed PID protocol in ensuring the leader-tracking as well as the boundedness of the adaptive control gains. Numerical simulations, involving both the synchronization control problem for nonlinear harmonic oscillators and the practical engineering problem of the cooperative driving for autonomous connected vehicles, confirm the theoretical derivation and disclose the capability of the proposed strategy in achieving the control objective.
... Later on, in [22] a linear quadratic control method was adopted for computing output synchronizing protocols. In [23], an L 2 -gain output synchronization problem was addressed by casting this problem into a number of L 2 -gain stabilization problems for certain linear systems, where the state space dimensions of these systems are equal to that of the agents. In [24], a modelfree approach based on reinforcement learning algorithms was proposed to obtain output synchronizing protocols, see also [25]. ...
... It was shown in [18] that solvability of certain regulator equations is necessary for output synchronization of heterogeneous linear multi-agent systems, see also [19,23,30] and [31]. Following up on this, throughout this paper we make the standard assumption that there exists a positive integer r such that the regulator equations ...
... Thus we have (23), and the conclusion then follows from Lemma 3. □ ...
This paper deals with the H2 suboptimal output synchronization problem for heterogeneous linear multi-agent systems. Given a multi-agent system with possibly distinct agents and an associated H2 cost functional, the aim is to design output feedback based protocols that guarantee the associated cost to be smaller than a given upper bound while the controlled network achieves output synchronization. A design method is provided to compute such protocols. For each agent, the computation of its two local control gains involves two Riccati inequalities, each of dimension equal to the state space dimension of the agent. A simulation example is provided to illustrate the performance of the proposed protocols.
... Later on, in [22] a linear quadratic control method was adopted for computing output synchronizing protocols. In [23], an L 2 -gain output synchronization problem was addressed by casting this problem into a number of L 2 -gain stabilization problems for certain linear systems, where the state space dimensions of these systems are equal to that of the agents. For related work, we also mention [24], [25] and [26], to name a few. ...
... [18], [19] and [21]. It was shown in [18] that solvability of certain regulator equations is necessary for output synchronization of heterogeneous linear multi-agent systems, see also [19], [23], [26] and [28]. Following up on this, throughout this paper we make the standard standing assumption that there exists a positive integer r such that the regulator equations ...
... Thus we have (23), and the conclusion then follows from Lemma 3. ...
This paper deals with the H2 suboptimal output synchronization problem for heterogeneous linear multi-agent systems. Given a multi-agent system with possibly distinct agents and an associated H2 cost functional, the aim is to design output feedback based protocols that guarantee the associated cost to be smaller than a given upper bound while the controlled network achieves output synchronization. A design method is provided to compute such protocols. For each agent, the computation of its two local control gains involves two Riccati inequalities, each of dimension equal to the state space dimension of the agent. A simulation example is provided to illustrate the performance of the proposed protocols.
... proposed to enhance the stability of microgrids under FDI attacks [16][17][18][19][20][21][22][23]. In [16], an elastic distributed control algorithm is proposed. ...
... The algorithm first detects the existence of attacks, then gradually strips the attacked DG from the communication network. In [17][18][19], the influence of limited numbers of attackers on microgrids is regarded as interference. Striping the frequency information of the system from noise is investigated to solve the microgrid defense problem. ...
To alleviate the hassle of false data injection (FDI) attacks on distributed generators (DGs) in microgrids, a communication encryption-based distributed cooperative control is proposed in this paper. Compared to the conventional distributed control strategies, the proposed control scheme is simpler with much less complex evaluation mechanism by upgrading the secondary control to a second-order control based on the finite-time control theory while combining an encryption strategy. The proposed algorithm provides constant injections to eliminate the impact of FDI attacks based on a robust communication system. The effectiveness and high efficiency of the proposed control scheme is validated in an IEEE 34 Node Test Feeder system with six DGs as a microgrid cyber-physical system (CPS) under different FDI attacks.
... This method was used for the static output feedback synthesis of the quadrotor flight control in cases when the quadrotor with its control system was considered a holonomic system [9], and a nonholonomic system as well [10]. It is necessary to note also, that in [11] the method was applied for control of the quadrotor formation flight. ...
... Therefore, the goal of this article is the creation of an algorithm for information processing using the application of the 2 L -gain minimization method for the development of the discrete control algorithm for the quadrotor control system. Results obtained in [7,8,11] are based on the usage of the algebraic Riccati equation for continuous systems. However, the algebraic Riccati equation for the discrete systems differs essentially from the algebraic Riccati equation, therefore results of [7,8] cannot be applied in this case. ...
... M ∈ R m×m andR ∈ R q×m are two constant matrices. Traditionally, the following output feedback controller was designed [39]: ...
... In this example, a three-order LTI model in [39] is adopted to describe the dynamic model of the mobile stage vehicles, where x i (t) = x 1i (t) x 2i (t) x 3i (t) T , and x 1i (t), ...
... Disturbance attenuation approaches focus on minimizing the effects of disturbance on the local neighborhood tracking error [41]- [42]. More specifically, the H ∞ approach for DMAS (1) in presence of disturbance w i (k) designs a distributed control protocol as in (3), such that the desired consensus is achieved as in (8), if disturbance w i (k) = 0 and the bounded L 2 -gain condition is fulfilled for any disturbance ...
This work presents a rigorous analysis of the adverse effects of cyber-physical attacks on discrete-time distributed multi-agent systems, and propose a mitigation approach for attacks on sensors and actuators. First, we show how an attack on a compromised agent can propagate and affect intact agents that are reachable from it. This is, an attack on a single node snowballs into a network-wide attack and can even destabilize the entire system. Moreover, we show that the attacker can bypass the robust control protocol and make it entirely ineffective in attenuating the effect of the adversarial input on the system performance. Finally, to overcome adversarial effects of attacks on sensors and actuators, a distributed adaptive attack compensator is designed by estimating the normal expected behavior of agents. The adaptive attack compensator is augmented with the controller and it is shown that the proposed controller achieves secure consensus in presence of the attacks on sensors and actuators. This controller does not require to make any restrictive assumption on the number of agents or agent's neighbors under direct effect of adversarial input. Moreover, it recovers compromised agents under actuator attacks and avoids propagation of attacks on sensors without removing compromised agents. The effectiveness of the proposed controller and analysis is validated on a network of Sentry autonomous underwater vehicles subject to attacks under different scenarios.
... 3) Scenario 3: The microgrid is under cyber-attack, and it is protected by the proposed secure state estimation (Fooladivanda et al. 2019). Other scholars mentioned "noise filtration" (Basseville and Nikiforov 1993) or "disturbance attenuation techniques" (Jiao et al. 2016) to detect and remove malicious attacks. Diversity of cyber-attacks led to creation of different detection and defense methods and mechanisms. ...
Security of the Internet and online communication has become an essential challenge in contemporary world. Paper discusses different types of cyber threats: cyber-attack, cyber terrorism and cybercrime. Individuals, companies and the states rely their communication and daily functioning on information and communication technologies (ICT). The purpose of the study is to highlight importance of the ICT safety use by pointing to seriousness of the cyber threats. The main methods applied in paper to examine published scientific materials are: inductive and deductive method, analytical and synthesis method, hypothetical-deductive method and method of content analysis. Results of the study indicate need for actively dealing with cyber threats. The intent of this study is both to inform and raise awareness of cyber threats within the communities. Findings of the study contribute to the broader knowledge in research area.
... Reference [16] proposes an elastic distributed control method, which firstly judges whether DG is attacked or not, and then it gradually strips the attacked DG from the communication network through calculation. References [17] - [19] regard the influence of a limited number of attackers on the system as noise interference. Striping the frequency information of the system from noise is studied to solve the microgrid CPS defense problem. ...
A new privacy-preserving algorithm based on the Paillier cryptosystem including a new cooperative control strategy is proposed in this paper, which can resist the false data injection (FDI) attack based on the finite-time control theory and the data encryption strategy. Compared with the existing algorithms, the proposed privacy-preserving algorithm avoids the direct transmission of the ciphertext of frequency data in communication links while avoiding complex iterations and communications. It builds a secure data transmission environment that can ensure data security in the AC microgrid cyber-physical system (CPS). This algorithm provides effective protection for AC microgrid CPS in different cases of FDI attacks. At the same time, it can completely eliminate the adverse effects caused by the FDI attack. Finally, the effectiveness, security, and advantages of this algorithm are verified in the improved IEEE 34-node test microgrid system with six distributed generators (DGs) in different cases of FDI attacks.
... Cyber attacks can be modeled as noise or disturbance to the system. Basseville et al. (Basseville and Nikiforov, 1993) use noise filtration techniques to detect and remove malicious attacks, and the authors in Jiao et al. (2016) develop disturbance attenuation methods for cyber attack detection. Notice that noise filtration or disturbance attenuation techniques operate under certain statistical properties, e.g., white Gaussian noise signal. ...
A timely, accurate, and secure dynamic state estimation is needed for reliable monitoring and efficient control of microgrids. The synchrophasor technology enables system operators to obtain synchronized measurements in real-time and to develop dynamic state estimators for monitoring and control of microgrids. However, in practice, sensor measurements can be corrupted or attacked. In this study, we consider an AC microgrid comprising several synchronous generators and inverter-interface power supplies, and focus on securely estimating the dynamic states of the microgrid from a set of corrupted data. We propose a secure dynamic state estimator which allows the microgrid operator to reconstruct the dynamic states of the microgrid from a set of attacked or corrupted data without any assumption on attacks or corruptions. Finally, we consider an AC microgrid with the same topology as the IEEE 33-bus distribution system, and show that the proposed secure estimation algorithm can accurately reconstruct the attack signals.
... The design of the hierarchical platoon controller (6) and (7) is based on the output synchronization control [27] [28], which requires the following regulator equation to be satisfied: ...
... Preliminary efforts probing cyber-attacks against the power systems would usually treat these attacks as a sort of noise or disturbance. So they tried their best to eliminate these disturbances using filtration techniques [31,32]. However, these techniques are based on pre-defined statistics which lose their effectiveness when facing slightly more fine tuned attacks [11]. ...
The importance of looking into microgrid security is getting more crucial due to the cyber vulnerabilities introduced by digitalization and the increasing dependency on information and communication technology (ICT) systems. Especially with a current academic unanimity on the incremental significance of the microgrid’s role in building the future smart grid, this article addresses the existing approaches attending to cyber-physical security in power systems from a microgrid-oriented perspective. First, we start with a brief descriptive review of the most commonly used terms in the latest relevant literature, followed by a comprehensive presentation of the recent efforts explored in a manner that helps the reader to choose the appropriate future research direction among several fields.
This paper presents a new model-free Q-learning approach to solve robust output consensus problems for heterogeneous multi-agent discrete-time (DT) systems. In connection with an auxiliary system, the problem is reformed to an augmented system including dynamics of agents and the leader. In this respect, we will consider a discounted performance criterion approach to obtain the solutions using RARE for developing a rigorous approach toward robust output consensus. We will also provide a lower bound on the discount factor that ensures stability of the closed-loop system, which is relevant for resilient performance against uncertainties. The Q-learning algorithm associated with the solution of RARE for an explicit model of the system's dynamics and, hence, is particularly suitable for real-world applications when such models may be unavailable or even incomplete. The proposed approach will also be proved to make the output regulation equations hold such that the tracking error converges to zero asymptotically. Comprehensive simulation examples are given to illustrate the effectiveness and robustness of the proposed approach by showing its potential to be implemented on various practical multi-agent systems.
This paper concerns the event-triggered distributed cross-dimensional formation control problem of heterogeneous multi-agent systems (HMASs) subject to limited network resources. The central aim is to design an effective distributed formation control scheme that will achieve the desired formation control objectives even in the presence of restricted communication. Consequently, a multi-dimensional HMAS is first developed, where a group of agents are assigned to several subgroups based on their dimensions. Then, to mitigate the excessive consumption of communication resources, a cross-dimensional event-triggered communication mechanism is designed to reduce the information interaction among agents with different dimensions. Under the proposed event-based communication mechanism, the problem of HMAS cross-dimensional formation control is transformed into the asymptotic stability problem of a closed-loop error system. Furthermore, several stability criteria for designing a cross-dimensional formation control protocol and communication schedule are presented in an environment where there is no information interaction among follower agents. Finally, a simulation case study is provided to validate the effectiveness of the proposed formation control protocol.
This article investigates the leader-following secure output consensus (LFSOC) problem of the heterogeneous multiagent systems (MASs) under the hybrid cyber-attacks. A novel hybrid cyber-attack model consisting of aperiodic additive deception (AAD) attacks and aperiodic denial of service (ADoS) attacks is proposed for characterizing cyber-attacks in a real network, where the aperiodicity is reflected in the fact that the duration of each cyber-attack can be different. First, a compensator is introduced for each agent to estimate the leader’s state. Second, two sampling mechanisms consisting of a multirate sampling (MRS) mechanism and a periodic sampling mechanism are employed for heterogeneous MASs. The MRS mechanism is used to obtain real-time sampled data on the different physical variables of each agent. The periodic sampling mechanism is applied to sample the agents’ compensators and the sampled data are broadcast to their neighbors immediately through a network. By selecting an appropriate sampling period (i.e., a communication period of the compensators), the robustness of heterogeneous MASs against hybrid cyber-attacks can be enhanced. Then, the appropriate communication period is selected for the compensators in different network environments by taking into consideration the cyber-attack parameters. Under these two sampling mechanisms, a sync controller is developed to achieve the LFSOC of heterogeneous MASs. Finally, an example is presented to verify the effectiveness of the proposed approach.
This article investigates the leader-following output consensus (LFOC) of the uncertain heterogeneous multi-agent systems (MASs) under a multirate sampling (MRS) mechanism and multi-channel hybrid (MCH) cyber-attacks by using an internal model principle. A novel form of cyber-attacks called MCH cyber-attacks is introduced, which encompasses distributed Denial of Service (DDoS) attacks and distributed deception (DD) attacks. First, we devise an MRS mechanism to sample real-time outputs from each agent with multiple physical properties. A multirate observer for each agent to fuse the sampled-data at different rates while reconstructing the agents’ states. Second, we develop an edge-based dynamic event-triggered mechanism (DETM) with flexibility and high scalability to alleviate the communication burden. The triggering conditions of this mechanism can be adjusted in real-time based on the requirements of each communication channel. With the multirate observer and edge-based DETM, we construct a fully distributed observer-based controller for each agent. Under this controller, the LFOC problem of uncertain heterogeneous MASs subject to the MCH cyber-attacks can be solved in a fully distributed manner, while ensuring the exclusion of the Zeno behaviors. Finally, a simulation example is presented to validate the effectiveness of the proposed method.
In this paper, we explore the consensus of positive networked systems with actuator faults. Firstly, the undirected and strongly connected topology is established with graph theory. The positive system theory is used to analyze the positive consensus of the closed-loop networked systems. State feedback gains are derived utilizing Algebraic Riccati Inequalities. Bounded multiplicative faults are regarded as uncertainties in the system matrix, while treating additive faults as external disturbances. Further, this transformation refocuses the analysis on the consensus problem with an L2-gain. Subsequently, the Genetic Algorithm is employed to optimize the L2 performance criteria. Finally, the effectiveness of the proposed theory is validated through simulations involving both single-input electric circuit systems and multi-input networked systems.
Multiple leader and follower graphical games constitute challenging problems for aerospace and robotics applications. One of the challenges is to address the mutual interests among the followers with an optimal control point of view. In particular, the traditional approaches treat the output containment problem by introducing selfish followers where each follower only considers their own utility. In this article, we propose a differential output containment game over directed graphs where the mutual interests among the followers are addressed with an objective functional that also considers the neighboring agents. The obtained output containment error system results in a formulation where outputs of all followers prove to converge to the convex hull spanned by the outputs of leaders in a game optimal manner. The output containment problem is solved using the
output feedback method, where the new necessary and sufficient conditions are presented. Another challenge is to design distributed Nash equilibrium control strategies for such games, which cannot be achieved with the traditional quadratic cost functional formulation. Therefore, a modified cost functional that provides both Nash and distributed control strategies in the sense that each follower uses the state information of its own and neighbors is presented. Furthermore, an
gain bound of the output containment error system that experiences worst-case disturbances with respect to the
criterion is investigated. The proposed methods are validated by means of multiagent quadrotor unmanned aerial vehicles output containment game simulations.
In this paper, we investigate a finite-time output regulation (FTOR) problem for linear heterogeneous multi-agent systems (LHMAS). The objective is to design protocols such that each agent can follow the reference signal within a finite time. An exosystem is given to generate the reference signal and disturbances. Only a part of agents are assumed to have access to the system matrix and state of the exosystem. First, smooth distributed finite-time observers are designed to estimate them. Then, with the help of feedforward method, smooth state feedback and output feedback controllers are designed to address the FTOR problem. By virtue of the finite-time control method and the OR technique, it is shown that the proposed smooth distributed observers and controllers can achieve the finite-time convergence of the estimation errors and error outputs, respectively. Finally, a numerical example is presented for illustration.
The fault-tolerant consensus control for heterogeneous multi-agent systems with actuator faults and external disturbances is studied in this paper. Firstly, considering the unknown actuator fault information and the influence of external disturbance on the observer, a robust sliding mode observer with adaptive laws modification was proposed to realize the actuator fault reconstruction. Secondly, a fault-tolerant controller is designed based on the reconstructed values obtained from the adaptive robust sliding mode observer, and the original heterogeneous complex dynamic high-dimensional system is converted into two low-dimensional closed-loop error systems by decoupling method. Furthermore, Lyapunov and Ricatti theories are used to obtain the controller gain solution method. Finally, a simulation experiment of fault-tolerant consensus control for heterogeneous multi-agent systems is carried out with one leading agent and four following agents, and the effectiveness and feasibility of the proposed method are verified.
This article studies the distributed cooperative control problem with the heterogeneous model structures and external disturbances for the connected vehicle (CV) platoon. We propose a hierarchical framework to separate information flow topology from local dynamics control, which aims to deal with the heterogeneous model structures of CV platoon. This hierarchical framework splits the control scheme into two layers, which include an observer in the upper-level layer and an integral sliding mode (ISM) controller in the lower-level layer. Then, the conditions for the asymptotic stability of the CV platoon are derived and the effectiveness of the ISM controller is demonstrated through the Lyapunov method. The research shows that compared with the traditional methods, the hierarchical framework does not need to specify the topology structure as a commonly used topology. Finally, numerical simulation results are performed to test the effectiveness and superiority of the developed controller.
The executions of protocols/algorithms for achieving second-order consensus are highly dependent on the communication networks, most of which have limited bandwidth and inherent vulnerability. This gives rise to complex network-induced phenomena which, in turn, bring great challenges to second-order consensus analysis. In order to alleviate network burden induced by limited communication capacity, ETSs have been proposed, under which information transmissions are triggered only when certain events occur, thereby significantly reducing the communication frequency [4].
This paper formulates a distributed static output feedback robust model predictive control for process networks to solve problems relating to unmeasured states and interconnected couplings. The initial conditions on the couplings are predicted by previous information and the boundedness of the predicted error is proved. In light of the static output feedback design conditions, the distributed static output feedback robust model predictive control is designed by transforming an infinite time optimization problem into a tractably solved one. The solvability of the optimization problem and the stability are proved to underpin the proposed approach. Simulations and an experimental case study are provided to validate the effectiveness of the proposed approach.
As one of the typical applications of connected vehicles (CVs), the vehicle platoon control technique has been proven to have the advantages of reducing emissions, improving traffic throughout and driving safety. In this paper, a unified hierarchical framework is designed for cooperative control of CVs with both heterogeneous model parameters and structures. By separating neighboring information interaction from local dynamics control, the proposed framework is designed to contain an upper-level observing layer and a lower-level tracking control layer, which helps address the heterogeneity in vehicle parameters and structures. Within the proposed framework, an observer is designed for following vehicles to observe the leading vehicle’s states using neighboring communication, while a tracking controller is designed to track the observed leading vehicle using local feedback control. Closed-loop stability in the absence and presence of communication time delay is analyzed, and the observer is further extended to a finite time convergent one to address string stability under general communication topology. Numerical simulation and field experiment verify the effectiveness of the proposed method.
This paper is concerned with the cross-dimensional formation control of a second-order multi-dimensional heterogeneous multi-agent system. Agents are first separated into several groups according to their position/velocity vector dimensions. Then the cross-dimensional formation control problem is formulated such that agents in the same group form a time-varying formation in their own dimension and agents in different groups cooperatively move in multiple dimensions. This can make follower agents in different dimensions cooperatively track a leader. Moreover, a cross-dimensional formation protocol is designed based on full or partial information of neighboring agents. For higher-dimensional agents, full information of lower-dimensional neighbors is adopted. For lower-dimensional ones, only partial information of higher-dimensional neighbors is used. Furthermore, a necessary and sufficient condition for the second-order heterogeneous multi-agent system to achieve cross-dimensional formation is provided. Accordingly, a criterion for designing cross-dimensional formation protocol is further derived. Finally, under an undirected graph, a lower-dimensional protocol design criterion is obtained if there is no data exchange between lower- and higher-dimensional followers. The effectiveness of the obtained results is demonstrated through cross-dimensional target enclosing performance analysis for multiple robots and quadrotors.
In this paper, the distributed fault-tolerant tracking control (FTTC) problems for uncertain homogeneous and heterogeneous multi-agent systems (MASs) under asynchronous sampled communications are investigated. In the case of asynchronous sampled communications, each agent is sampled at its own sampling instants and exchanges its sampling information to neighbor agents. In the presence of actuator failures, asynchronous sampled communications and different system dynamics, it is difficult to accomplish the task of distributed tracking control. To overcome this difficulty, two novel observer-based distributed FTTC protocols for uncertain homogeneous and heterogeneous MASs under asynchronous sampled communications are proposed. First, distributed observers are designed for each follower to estimate the leader's state under asynchronous sampled communications. Then, by virtue of the estimate, adaptive FTTC strategies are developed by utilizing the state feedback control and output feedback control, respectively. Finally, two simulation results are given to verify the theoretical results.
This paper addresses both the output leader-tracking and output containment control problems for heterogeneous linear high-order Multi-Agent Systems (MASs) sharing information over a directed communication topology and subject to external unknown disturbances. To solve these control problems, we propose a robust fully distributed Proportional-Integral-Derivative (PID) control strategy, equipped with a filter on the derivative action that allows obtaining both a simpler closed-loop formulation, without the need of the descriptor transformation, and good tracking performances in the case of fast reference signal behaviours. The stability analysis is analytically proven via the Lyapunov theory and the H∞ approach. The derived robust stability conditions are expressed as a set Linear Matrix Inequalities (LMIs) whose solution provides the proper tuning of the robust PID control gains. Numerical simulations confirm the effectiveness and robustness of the proposed approach in solving both the output leader-tracking and output containment control problems.
This article investigates the cooperative output regulation problem for discrete-time heterogeneous multiagent Markov jump systems. Two cases are studied: 1) output regulation quadratic control in the case where the exosystem is accessible to all agents and 2) cooperative output regulation quadratic control in the case where only a part of agents can directly communicate with the exosystem. The hidden Markov models are employed to describe the asynchronous modes of the agents and their corresponding controllers. Via the jumping regulator equation, asynchronous control laws are constructed and the algorithms to obtain control parameters are presented in terms of linear matrix inequalities. For the first case, the optimal synchronous/mode-dependent control law, which is a special case of the asynchronous control protocol, is also given via the stochastic dynamic programming approach. Finally, an example is given to illustrate the effectiveness of the proposed approaches.
This paper studies the distributed fault-tolerant control (FTC) problem for heterogeneous nonlinear multi-agent systems (MASs) under sampled intermittent communications. First, in order to estimate the state of leader under sampled intermittent communications, the distributed intermittent observer for each follower is constructed. By using the tool from switching system theory, the estimation error converges to zero exponentially if the communication rate is larger than a threshold value even under the impact of sampled intermittent communications. Then, by applying model reference adaptive tracking technique, a robust FTC protocol is developed to track the distributed intermittent observer. Two algorithms are presented to choose the feedback gain of the distributed intermittent observer and the tracking feedback gain of the fault-tolerant tracking controller. It is proved that the global consensus tracking error is bounded under the developed distributed control protocol. Finally, an example with the coupled pendulums is provided to verify the efficiency of the designed method.
In this study, the distributed output consensus control issue is investigated for a class of linear cluster multi-agent systems (CMASs) under the control strategy of the reset observer. We consider a communication network consisting of several clusters, each of which is directed and contains a leader. The interactions among agents include continuous-discrete hybrid communication. Specifically, an instantaneous connectivity only exists between the clusters at discrete moments, called the reset time sequence. At the reset time, an instantaneous fixed directed network is formed such that only the leaders will consider the available information of neighboring leaders to reset their own states. During non-reset intervals, only the intra-clusters are connected while the inter-clusters are equivalent to a disconnected network topology. Considering that in practice, the state information may be partially unavailable, only the relative output information is utilized to estimate the unavailable state and thus control protocols are developed with the help of the reset full-order and reduced-order observers, respectively. The stability of the closed-loop CMAS at both the reset time and non-reset intervals is studied based on Lyapunov analysis. The consensus value depends only on the initial conditions and the network topology involved, and not on the reset time sequence. Finally, numerical simulations are provided to illustrate the theoretical results.
This paper revisits the sampled-data cooperative
output regulation (COR) problem in a hybrid system framework.
Due to the inevitable network-induced imperfections caused by
communication among agents, we consider the problem under
asynchronous transmissions and time-varying delays. A hybrid
system model is introduced to incorporate the aforementioned
communication imperfections and facilitate the analysis on internal
stability and L2 (L1) performance of closed-loop systems. A
novel Lyapunov functional candidate is proposed to establish the
stability condition in terms of maximally allowable transmission intervals
(MATIs) and maximally allowable delays (MADs). Compared
with some existing results, the proposed Lyapunov functional
candidate provides clearer physical significance. As a result, more
straightforward computations and trade-off designs on MATIs and
MADs can be provided. Finally, numerical simulations are given to
illustrate the efficiency and feasibility of the obtained results.
This paper considers a bipartite output synchronization problem for heterogeneous linear multi-agent systems with time-varying communication networks using an adaptive distributed observer-based control strategy. Based on the relative output information from neighboring agents, a reduced-dimensional distributed observer is proposed to estimate the unavailable state information of each agent. Meanwhile, an edge-based adaptive law is designed for each agent to assign the time-varying interaction weight such that the connectivity of the communication network is preserved. Theoretical analysis is presented for the convergence of the output tracking errors under the proposed output feedback control strategy. Some numerical results are also presented to validate the proposed control strategy.
In this paper, the containment control problem of heterogeneous uncertain high-order linear Multi-Agent Systems (MASs) is addressed and solved via a novel fully-Distributed Model Reference Adaptive Control (DMRAC) approach, where each follower computes its adaptive control action on the basis of local measurements, information shared with neighbors (within the communication range) and the matching errors w.r.t. its own reference model, without requiring any previous knowledge of the global directed communication topology structure. The approach inherits the robustness of the direct model reference adaptive control (MRAC) scheme and allows all agents converging towards the convex hull spanned by leaders while fulfilling at the same time local additional performance requirements at single-agent level, such as prescribed settling time, overshoot, etc. The asymptotic stability of the whole closed-loop network is analytically derived by exploiting the Lyapunov theory and the Barbalat lemma, hence proving that each follower converges to the convex hull spanned by the leaders, as well as the boundedness of the adaptive gains. Extensive numerical analysis for heterogeneous MAS composed of stable, unstable and oscillating agent dynamics are presented to validate the theoretical framework and to confirm the effectiveness of the proposed approach.
In this paper, the problem of leader-following consensus is investigated for general linear multi-agent systems under external disturbances. The communication topologies in the system are time-varying and switched from a finite set. To model these topologies, a signal with average dwell time switching is introduced. Then the overall closed-loop system is described as a switched control system. The notion of weighted L 2 - L ∞ performance is then introduced and analyzed. Based on the local information obtained from the neighbours, a topology-dependent controller is designed. The asynchronous switching in this paper means that the switchings between the communication topologies and the controllers are asynchronous. Conditions are developed for the existence of a control protocol to produce the leader-following consensus with a certain level of weighted L 2 − L ∞ performance. The design algorithm is then formulated as a set of linear matrix inequalities (LMIs). A numerical example is then given to show the effectiveness of the proposed consensus algorithm.
This paper addresses the leader-tracking and the containment control problems for heterogeneous high-order Multi-Agent Systems (MASs) sharing information through a directed communication topology. To solve both the control problems, a fully-distributed Proportional-Integral-Derivative (PID) control strategy is proposed, whose stability is analytically proven by exploiting the regulator equations and the Static Output Feedback (SOF) procedure adapted to the MASs framework. The application of SOF allows recasting the PID control design problem into a state-feedback control design one and, hence, finding the proper values of the proportional, integral and derivative actions via classical state-feedback approaches, such as the Linear-Quadratic-Regulator (LQR) strategy. Numerical simulations confirm the effectiveness of the proposed approach in guaranteeing that each follower tracks the leader behavior in the case of leader-tracking and that each follower converges to the convex hull spanned by the multiple leaders in the case of containment control.
In this paper we consider the synchronization problem in a network of nonlinear multi-agent systems having the same relative degree
r
. The agents do not have access to their state or output and only have relative output information from their neighbors. The controller structure is decentralized in nature and therefore depends only on the relative information available to it. The agent dynamics are transformed into the relative dynamics by a change of coordinates where the agents are coupled. Extended high-gain observers are used to estimate the nonlinear coupling at each agent and then cancel them using feedback control. Therefore, the problem changes to a stabilization of
N
nonlinear systems in the relative coordinates. It is shown that the agents achieve practical synchronization and the synchronization error can be made arbitrarily small by tuning the high-gain observer parameter. Finally, simulations are done with a network of power systems to show the efficacy of the proposed controller.
The problem of robust leader‐following consensus of heterogeneous multiagent systems subject to deny‐of‐service attacks is investigated, where attack strategies are partially unknown and uncertain to defender. A Markovian jump system approach is proposed, that is, capable of describing the occurrence of different attack strategies, and the occurring probability of each attack strategy is represented by the transition probability of the Markovian jump model. Then, sufficient conditions are derived such that the output tracking performance can be guaranteed. In order to design the controller gains, some slack matrices are introduced, which can provide some design freedom. Finally, it is shown that the controller design results can be applied to the multivehicle position‐tracking system. The simulation results reveal that the consensus performance is much better if one has more statistics information on attacks.
The optimal solution to the leader-follower bipartite output synchronization problem is proposed for heterogeneous multiagent systems (MASs) over signed digraphs in the presence of adversarial inputs in this article. For the MASs, the dynamics and dimensions of the followers are different. Distributed observers are first designed to estimate the leader's two-way state and output over signed digraphs. Then, the leader-follower bipartite output synchronization problem on signed graphs is translated into a conventional output distributed leader-follower problem over nonnegative graphs after the state transformation by using the information of followers and observers. The effect of adversarial inputs in sensors or actuators of agents is mitigated by designing the resilient H
∞
controller. A data-based reinforcement learning (RL) algorithm is proposed to obtain the optimal control law, which implies that the dynamics of the followers is not required. Finally, a simulation example is given to verify the effectiveness of the proposed algorithm.
This article addresses the distributed H∞ consensus problem of multi-agent systems with general linear node dynamics using relative output measurements. The notion of H∞ consensus performance region is first introduced and then analysed as a basis for the protocol design. A new kind of distributed observer-type H∞ protocols is further proposed. Theoretical analysis indicates that the distributed H∞ consensus problem can be solved if and only if the coupling strength of the protocol belongs to the H∞ performance region of the closed-loop network. Finally, some numerical simulations are provided to illustrate the effectiveness of the theoretical results.
This article addresses the consensus problem for cooperative multiple agents with nonlinear dynamics on a fixed directed information network, where each agent can only communicate with its neighbours intermittently. A class of control algorithms is first introduced, using only intermittent relative local information. By combining tools from switching systems and Lyapunov stability theory, some sufficient conditions are established for consensus
of multi-agent systems without any external disturbances under a fixed strongly connected topology. Theoretical analyses are further provided for consensus of multi-agent systems in the presence of external disturbances. It is shown that a finite L2-gain performance index for the closed-loop multi-agent systems can be guaranteed if the coupling strength of the network is larger than a threshold value determined by the average communication rate
and the generalised algebraic connectivity of the strongly connected topology. The results are then extended to consensus with prescribed L2-gain performance with a virtual leader where the underlying topology is not necessarily strong connected or contain a directed spanning tree. Numerical simulations are finally provided to verify and visualise the theoretical analysis.
This technical note studies synchronization of identical general linear systems on a digraph containing a spanning tree. A leader node or command generator is considered, which generates the desired tracking trajectory. A framework for cooperative tracking control is proposed, including full state feedback control, observer design and dynamic output feedback control. The classical system theory notion of duality is extended to networked systems. It is shown that unbounded synchronization regions that achieve synchronization on arbitrary digraphs containing a spanning tree can be guaranteed by using linear quadratic regulator based optimal control and observer design methods at each node.
Consensusability of multi-agent systems (MASs) is a fundamental problem in the MAS research area, since when starting to design a consensus protocol, one should know whether or not there exists such a protocol that has the ability to make the MAS involved consensus. This technical note is aimed at studying the joint impact of the agent dynamic structure and the communication topology on consensusability. For the MASs with fixed topology and agents described by linear time-invariant systems, a necessary condition of consensusability with respect to a set of admissible consensus protocols is given, which is shown, under some mild conditions, to be necessary and sufficient.
This paper studies state synchronization of multi-agent systems with disturbances using distributed static output-feedback (OPFB) control. The bounded gain synchronization problem using distributed static OPFB is defined and solved. The availability of only output measurements restricts the local controls design, while the communication graph topology restricts global information flow among the agents. It is shown here that these two types of restriction can be dealt with in a symmetric manner and lead to two similar conditions guaranteeing the existence of bounded gain static OPFB. One condition is on the output measurement matrix on a local scale, and the other on the graph Laplacian matrix on a global scale. Under additional conditions a distributed two-player zero-sum game using static OPFB is also solved and leads to distributed Nash equilibrium on the communication graph. As a special case the static OPFB globally optimal control is given. A new class of digraphs satisfying the above condition on the graph Laplacian is studied. The synchronizing region for distributed static OPFB control is exposed and found to be conical, different than the infinite right-half plane synchronizing region for distributed state feedback.
This paper concerns the problem of distributed controller synthesis for a class of heterogeneous distributed systems composed of αα (22 or more) different kinds of subsystems, interacting with one another according to a certain given graph topology. We will show that by employing Linear Matrix Inequalities (LMIs) tools, namely the full-block S-procedure, we can derive a control synthesis method based on L2L2 gain performance. This synthesis method guarantees stability and performance of a whole set of possible interconnection graphs, and its computational complexity does not depend on the number of subsystems involved but only on the number of different kinds of subsystems. The effectiveness of the new method is verified on a test case.
The synchronisation problem is investigated for multiple linear agents with external disturbances that are guided by a leader with different dynamics. A method is presented for designing a networked controller that synchronises the agents. First, a general dynamic controller with two inputs is proposed that introduces the model of the leader as an internal reference model into the control loop of all the following agents. Second, the two inputs to the local controllers of the followers are designed by H ∞ control theory such that the resulting closed-loop system achieves the output synchronisation with a desired disturbance attenuation performance. The proposed method is applied to the leader–follower synchronisation of vehicles in a platoon.
In this note, the cooperative output regulation problem of heterogeneous linear multi-agent systems is investigated. Our approach is based on internal model and dynamic error feedback among the agents. Under some standard assumptions, the problem is solved by an internal model and a stabilizing H∞ controller. We showed that the exo-signal-free system is stabilized if each controlled agent is robust (in the sense of H∞ norm) to resist the disturbance measured by the second largest eigenvalue of the graph adjacency matrix. Then the synthesis problem is solved using algebraic Riccati equation. Furthermore, we showed that this condition is a generalization of existing results.
The task of synchronizing autonomous agents is solved by a networked controller that steers the agents towards a common trajectory. This technical note extends existing analysis and design methods towards sets of linear agents with individual dynamics. A necessary and sufficient synchronization condition is proved and it is shown that the agents can be synchronized by an appropriate networked controller if and only if their dynamics intersect.
This paper brings forward the notion of “H∞H∞ almost output synchronization” for heterogeneous multi-agent systems under directed interconnection structures. Agents are assumed to be linear, right-invertible and introspective (i.e. agents have partial knowledge of their own states). The objective is to suppress the impact of disturbances on the synchronization error dynamics in terms of the H∞H∞ norm of the corresponding closed-loop transfer function. In addition, the problem of regulating the consensus trajectories to a reference signal is addressed. The application of the proposed method to the problem of formation is furthermore elucidated. Simulation results are provided to illustrate the method.
This paper reviews the static output feedback problem in the control of linear, time-invariant (LTI) systems. It includes analytical and computational methods and presents in a unified fashion the knowledge gained in the decades of research into this important open problem. The paper shows that although many approaches and techniques exist to approach different versions of the problem, no efficient algorithmic solutions are available.
This paper addresses the distributed H2H2 and H∞H∞ control problems for multi-agent systems with linear or linearized dynamics. An undirected multigraph with loops is used to represent the communication topology of a multi-agent network. A distributed controller is designed, based on the relative states of neighboring agents and a subset of absolute states of the networked agents. The notions of H∞H∞ and H2H2 performance regions are introduced and analyzed, respectively. A necessary and sufficient condition for the existence of a controller yielding an unbounded H∞H∞ performance region is derived. A multi-step procedure for suboptimal H∞H∞ controller synthesis is presented. It is also shown that the H∞H∞ performance limit of the network under the distributed controller is equal to the minimal H∞H∞ norm of a single agent achieved by using the state feedback controller. It is finally shown that, contrarily to the H∞H∞ case, the H2H2 performance limit scales with the number of agents in the network.
Necessary and sufficient conditions are presented for static output-feedback control of linear time-invariant systems using the H-infinity approach. Simplified conditions are derived which only require the solution of two coupled matrix design equations. It is shown that the static output-feedback H-infinity solution does not generally yield a well-defined saddle point for the zero-sum differential game; conditions are given under which it does. This paper also proposes a numerically efficient solution algorithm for the coupled design equations to determine the output-feedback gain. A major contribution is that an initial stabilizing gain is not needed. An F-16 normal acceleration design example is solved to illustrate the power of the proposed approach.
In this paper we study lth-order (l >= 3) consensus algorithms, which generalize the existing first-order and second-order consensus algorithms in the literature. We show necessary and sufficient conditions under which each information variable and its higher-order derivatives converge to common values. We also present the idea of higher-order consensus with a leader and introduce the concept of an lth-order model-reference consensus problem, where each information variable and its high-order derivatives not only reach consensus, but also converge to the solution of a prescribed dynamic model. The effectiveness of these algorithms is demonstrated through simulations and a multivehicle cooperative control application, which mimics a flocking behavior in birds.
We consider the design of a decentralized controller for a linear time invariant (LTI) system. This system is modelled as an interconnection of subsystems. For every subsystem, a linear time invariant controller is sought such that the overall closed loop system is stable and achieves a given H performance level. The main idea is to design every local controller such that the corresponding closed loop subsystem has a certain input-output (dissipative) property. This local property is constrained to be consistent with the overall objective of stability and performance. The local controllers are designed simultaneously, avoiding the traditional iterative process: both objectives (the local one and the global one) are achieved in one shot. Applying this idea leads us to solving the following new problem: given an LTI system, parameterize all the dissipative properties which can be achieved by feedback. The proposed approach leads to solving convex optimization problems that involve linear matrix inequality constraints.
This paper addresses the distributed H∞ consensus problem of linear or linearized multi-agent systems subject to external disturbances. A distributed consensus protocol is proposed, based on the relative states of neighboring agents. The distributed H∞ consensus problem of such a multi-agent network is cast into the H∞ control problem of a set of independent systems having the same dimension as that of a single agent. The notion of H∞ consensus region is then introduced and analyzed. A necessary and sufficient condition for the existence of a protocol having an unbounded H∞ consensus region is derived. A multi-step procedure is further presented for constructing such a protocol. It is shown that the H∞ performance limit of the consensus of the multi-agent network is equal to the minimal H∞ norm of a single agent achieved by using a state feedback controller.
This article is devoted to the consensus control for switching networks of multiple agents with linear coupling dynamics and subject to external disturbances, which is transformed into an H∞ control problem by defining an appropriate controlled output. On this basis, a distributed dynamic output feedback protocol is proposed with an undetermined system matrix, and a condition in terms of linear matrix inequalities (LMIs) is derived to ensure consensus of the multi-agent system with a prescribed H∞ level. Furthermore, system matrix of the protocol is designed by solving two LMIs. A numerical example is included to illustrate the effectiveness of the proposed consensus protocol.
This paper deals with the consensus control of a multi-agent system with state and measurement disturbances, and proposes a distributed dynamic output feedback protocol. By defining an appropriate controlled output, the consensus control problem is reformulated as an Hinfin control problem. Using Hinfin techniques, a sufficient condition in terms of linear matrix inequalities (LMIs) is given to ensure consensus with the prescribed Hinfin performance, and the undetermined system matrix of the proposed protocol is obtained. Simulation results show that a multi-agent system under the proposed protocol with system matrix solved by the LMI (linear matrix inequality) approach possesses the desired Hinfin consensus performance.
In this paper, we consider the cooperative output regulation of linear multi-agent systems. The overall system consists of two groups of subsystems. While the first group of subsystems can access the exogenous signal, the second cannot. As a result, the problem cannot be solved by the decentralized approach. By devising a distributed observer, we can solve the problem by a dynamic full information distributed control scheme. The problem can also be viewed as a generalization of some leader-following consensus problems of multi-agent systems.
This paper addresses the global consensus problem of multi-agent systems with a leader-follower communication topology consisting of Lur'e type of node dynamics. A decomposition approach is proposed to convert the consensus of a high-dimensional Lur'e network into the test of a set of matrix inequalities whose dimensions are the same as a single node system. The notion of global consensus region is then introduced and analyzed. A necessary and sufficient condition is derived for the existence of a consensus protocol to guarantee a desirable unbounded consensus region. A multi-step design procedure is given for constructing such a consensus protocol, which maintains a favorable decoupling property. The effectiveness of the theoretical results is demonstrated through a network of Chua's circuits.
This paper investigates consensus problems for directed networks of agents with external disturbances and model uncertainty on fixed and switching topologies. Both networks with and without time-delay are taken into consideration. In doing the analysis, we first perform a model transformation and turn the original system into a reduced-order system. Based on this reduced-order system, we then present conditions under which all agents reach consensus with the desired H∞ performance. Finally, simulation results are provided to demonstrate the effectiveness of our theoretical results.
This paper presents a simplified parameterization of all H∞ static state-feedback controllers in terms of a single algebraic Riccati equation and a free parameter matrix. As a special case, necessary and sufficient conditions for the existence of an static output-feedback gain are given. An efficient computational algorithm is given and its correctness proven. No initial stabilizing output-feedback gain is needed. The technique is used to design an H∞ lateral–directional command augmentation system for the F-16 aircraft.
In this paper global stabilisation of a complex network is attained by applying local decentralised output feedback control to a minimum number of nodes of the network. The stabilisation of the network is treated as a rank constrained problem. Strict positive realness conditions on the node level dynamics allow nonlinearities/uncertainties which satisfy the sector conditions to be considered. A network of Chua oscillators with 75 nodes is considered to demonstrate the efficacy of the approach.
This paper is concerned with a leader–follower problem for a multi-agent system with a switching interconnection topology. Distributed observers are designed for the second-order follower-agents, under the common assumption that the velocity of the active leader cannot be measured in real time. Some dynamic neighbor-based rules, consisting of distributed controllers and observers for the autonomous agents, are developed to keep updating the information of the leader. With the help of an explicitly constructed common Lyapunov function (CLF), it is proved that each agent can follow the active leader. Moreover, the tracking error is estimated even in a noisy environment. Finally, a numerical example is given for illustration.
In this paper, we consider a multi-agent consensus problem with an active leader and variable interconnection topology. The state of the considered leader not only keeps changing but also may not be measured. To track such a leader, a neighbor-based local controller together with a neighbor-based state-estimation rule is given for each autonomous agent. Then we prove that, with the proposed control scheme, each agent can follow the leader if the (acceleration) input of the active leader is known, and the tracking error is estimated if the input of the leader is unknown.
In this paper, we discuss consensus problems for networks of dynamic agents with fixed and switching topologies. We analyze three cases: 1) directed networks with fixed topology; 2) directed networks with switching topology; and 3) undirected networks with communication time-delays and fixed topology. We introduce two consensus protocols for networks with and without time-delays and provide a convergence analysis in all three cases. We establish a direct connection between the algebraic connectivity (or Fiedler eigenvalue) of the network and the performance (or negotiation speed) of a linear consensus protocol. This required the generalization of the notion of algebraic connectivity of undirected graphs to digraphs. It turns out that balanced digraphs play a key role in addressing average-consensus problems. We introduce disagreement functions for convergence analysis of consensus protocols. A disagreement function is a Lyapunov function for the disagreement network dynamics. We proposed a simple disa
This paper addresses the consensus problem of multiagent systems with a time-invariant communication topology consisting of general linear node dynamics. A distributed observer-type consensus protocol based on relative output measurements is proposed. A new framework is introduced to address in a unified way the consensus of multiagent systems and the synchronization of complex networks. Under this framework, the consensus of multiagent systems with a communication topology having a spanning tree can be cast into the stability of a set of matrices of the same low dimension. The notion of consensus region is then introduced and analyzed. It is shown that there exists an observer-type protocol solving the consensus problem and meanwhile yielding an unbounded consensus region if and only if each agent is both stabilizable and detectable. A multistep consensus protocol design procedure is further presented. The consensus with respect to a time-varying state and the robustness of the consensus protocol to external disturbances are finally discussed. The effectiveness of the theoretical results is demonstrated through numerical simulations, with an application to low-Earth-orbit satellite formation flying.
The leader-following consensus problem of higher ordermulti-agent systems is considered. In the system, the dynamics of each agent and the leader is a linear system. The control of each agent using local information is designed and detailed analysis of the leader-following consensus is presented for both fixed and switching interaction topologies, which describe the information exchange between the multi-agent systems. The design technique is based on algebraic graph theory, Riccati inequality and Lyapunov
inequality. Simulations indicate the capabilities of the algorithms.
Output synchronization of a network of heterogeneous linear state–space models under time-varying and directed interconnection structures is investigated. It is shown that, assuming stabilizability and detectability of the individual systems and imposing very mild connectedness assumptions on the interconnection structure, an internal model requirement is necessary and sufficient for synchronizability of the network to polynomially bounded trajectories. The resulting dynamic feedback couplings can be interpreted as a generalization of existing methods for identical linear systems.
This work considers control design for distributed systems, where the controller is to adopt and preserve the distributed spatial structure of the nominal system. The specific feature of this work is that it does not require the underlying system dynamics to be homogeneous (shift invariant) with respect to spatial or temporal variables. Operator theoretic tools for working with these systems are developed, and lead to sufficient convex conditions for analysis and synthesis with respect to the ℓ2-induced norm.
We consider the problem of cooperation among a collection of vehicles performing a shared
task using intervehicle communication to coordinate their actions. We apply tools from graph theory to relate the topology of the communication network to formation stability. We prove a Nyquist criterion that uses the eigenvalues of the graph Laplacian matrix to determine the effect
of the graph on formation stability. We also propose a method for decentralized information
exchange between vehicles. This approach realizes a dynamical system that supplies each vehicle
with a common reference to be used for cooperative motion. We prove a separation principle
that states that formation stability is achieved if the information flow is stable for the given
graph and if the local controller stabilizes the vehicle. The information flow can be rendered
highly robust to changes in the graph, thus enabling tight formation control despite limitations
in intervehicle communication capability.
In a recent Physical Review Letters article, Vicsek et al. propose a simple but compelling discrete-time model of n autonomous agents (i.e., points or particles) all moving in the plane with the same speed but with different headings. Each agent's heading is updated using a local rule based on the average of its own heading plus the headings of its "neighbors." In their paper, Vicsek et al. provide simulation results which demonstrate that the nearest neighbor rule they are studying can cause all agents to eventually move in the same direction despite the absence of centralized coordination and despite the fact that each agent's set of nearest neighbors change with time as the system evolves. This paper provides a theoretical explanation for this observed behavior. In addition, convergence results are derived for several other similarly inspired models. The Vicsek model proves to be a graphic example of a switched linear system which is stable, but for which there does not exist a common quadratic Lyapunov function.
Parameterization of all stabilizing H∞ static state-feedback gains: application to output-feedback design
- Gadewadikar