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Finite-time consensus for multi-agent systems via terminal feedback iterative learning
IET Control Theory & Applications
Abstract
This study is devoted to the finite-time consensus problem of multi-agent systems with higher-order dynamics, and presents a framework for effectively constructing distributed protocols which incorporate iterative learning control actions into output feedbacks. Using a terminal updating law, the feedback iterative learning protocols are shown with the ability to enable all agents to achieve the consensus at a finite time that can be prescribed. Furthermore, a model reference approach is employed to improve the feedback iterative learning protocols such that all agents can be guaranteed to achieve the consensus at any given desired terminal output. In both cases, necessary and sufficient conditions are provided which can also offer design criteria for the learning gains to ensure consensus. Simulation results are included to verify the effectiveness of the proposed theoretical results.
... For instance, reference [24] developed two formation control algorithms utilizing iterative learning control (ILC). References [25]- [28] introduced an iterative learning output feedback protocol design framework and delved into the issue of exact consensus. References [29]- [32] explored iterative learning consensus based on NNs for unknown nonlinear MASs over finite intervals. ...
... Although consensus and ILCs within MASs have garnered significant scholarly interest, studies that combine these two areas are relatively scarce. Most of the existing literature predominantly concentrates on linear MASs [25]- [27] or systems with linear parameterizations [33]- [37]. Conversely, in the industrial setting, nonlinear parametric systems are just as prevalent. ...
... 2) In comparison to the existing body of related research, the model advanced in this paper exhibits a broader generality. Firstly, this study extends its scope to nonlinear MASs, in contrast to certain investigations that confine themselves to linear MASs (e.g., [25]- [27]). Secondly, this paper takes into account the influence of unmeasurable periodic disturbance parameters, which is different from the treatment of unknown nonlinear MASs [29]- [32]. ...
This paper tackles the exact consensus issue in nonlinearly parameterized multi-agent systems with unknown control directions, employing an adaptive learning control approach. The nonlinearly parameterized function is effectively compensated using neural networks and Fourier cardinal expansions. A cooperative consensus protocol is meticulously designed to achieve exact consensus through the application of iterative learning laws. The convergence of the consensus algorithm is rigorously analyzed using a composite energy function. Additionally, the robustness of the consensus algorithm is examined by introducing input disturbances to the controlled subsystem and bounded inputs to the leader. The scalability of the consensus protocol is explored through the context of formation control problems. Finally, the effectiveness of the constructed learning protocol is illustrated by simulations.
... The main result is given by the following Theorem 1. Theorem 1 : Consider a group of cloud connected leaderfollowers Euler-Lagrange systems (18), (6), (3) satisfy assumptions 1 to 3 and properties 1 to 6. Then, there exist linear consensus sliding vector (10) and protocol (29) with adaptive learning estimates (31) and achieve asymptotic consensus tracking provided that the interaction communication graph has a directed spanning tree. Proof: The proof of Theorem 1 has three parts. ...
... By adding and subtracting S T C a S and applying properties 1 to 6, assumptions 1 to 3 and protocol (29), (31),V a can be written aṡ ...
... Paper [14] studies secure consensus in synchronous networks under message manipulation attacks, and proposed a secure synchronous consensus algorithm based on two-hop neighboring information in the network. To avoid performance deterioration in distributed networks, Kailkhura et al. in [15] propose a weighted aver-connection topology, but also has prescribed terminal time as desired [24]. Owing to its simplicity and effectiveness, ILCbased consensus has generated considerable interest over the past years [25]- [29]. ...
... Since the nodes with extreme valuesα ij in the set ξ have been removed, the message received from the remaining nodes can directly store in the memory. Then, node i empties the data in M1 and is ready to receive the new data in the next time (Lines [24][25][26]. ...
This paper concentrates on the finite-time clock synchronization problem for wireless sensor networks (WSNs) under deception attacks. Compared with adding additional communication links to a network, we introduce a new mechanism termed as “trusted link” to improve the resilience of the network, and show that with small changes (set a fraction of links as the trusted links) in the network structure the network robustness for deception attacks can be improved significantly. Then, an iterative learning control based consensus control methodology with built-in attack mitigation mechanism is proposed. Not only the security and robustness are guaranteed by the proposed controller, but also the convergence time is fixed, which makes the synchronization algorithm more suitable for practical WSNs. Finally, simulation results are provided to demonstrate the effectiveness of the theoretical results.
... As is well-known, iterative learning control (ILC) can realize a high precise tracking on a finite interval [18]- [20] . In the past decade, researchers have utilized ILC to solve multiagent synchronization problems [21]- [26] . [21]- [23] earlier tried to achieve consistent tracking of multi-agent systems with iterative learning control method. ...
... In the past decade, researchers have utilized ILC to solve multiagent synchronization problems [21]- [26] . [21]- [23] earlier tried to achieve consistent tracking of multi-agent systems with iterative learning control method. [24] had achieved synchronization of multiple agents by means of adaptive iterative learning control. ...
... In multi-agent systems, inspired by the natural synchronization phenomena [28], the finite-time control schemes have been proposed based on the information measurements among the neighboring agents (e.g., [29], [30]). These control schemes are robust against perturbations and measurement errors and are faster than the conventional distributed control algorithm [31], [32]. From a practical perspective, sensitive loads in MGs require operation at the nominal voltage and frequency. ...
This paper presents a distributed fault-tolerant finite-time control algorithm for the secondary voltage and frequency restoration of islanded inverter-based Alternating
Current (AC) Microgrids (MGs) considering input saturation and faults. Most existing distributed methods commonly design the secondary control layer based on ideal conditions of the control input channels of the MG without any faults and disturbances. At the same time, MGs are exposed to actuator faults that can significantly impact the control of MGs and lead the MG to unstable situations. One of the other typical practical constraints in multi-agent systems such as MGs is saturation in some parts. The other novel idea is that a consensus-based scheme synchronizes the islanded MG’s voltage and
frequency to their nominal values for all DGs within finite time, irrespective of saturation and multiple faults, including partial loss of effectiveness and stuck faults simultaneously. Finally, the performance of the proposed control schemes is verified by performing an offline digital time-domain simulation on a test MG system through a couple of scenarios in the MATLAB/Simulink software environment. The effectiveness and accuracy of the proposed control schemes for islanded AC MGs are compared to previous studies, illustrating the privilege.
... Coordination and cooperative control of multi-client in distributed ML always attract lots of attention from various research communities, where a fundamental approach to achieve cooperative control is the consensus based algorithm [250]. Traditional consensus design are mostly based on single and finite-time domain [251], [252], where in reality, the dynamics of the system are usually complicated and non-linear. Therefore, a useful and effective consensus design with dynamic or unknown parameters is urgent in the future research. ...
Motivated by the advancing computational capacity of distributed end-user equipments (UEs), as well as the increasing concerns about sharing private data, there has been considerable recent interest in machine learning (ML) and artificial intelligence (AI) that can be processed on on distributed UEs. Specifically, in this paradigm, parts of an ML process are outsourced to multiple distributed UEs, and then the processed ML information is aggregated on a certain level at a central server, which turns a centralized ML process into a distributed one, and brings about significant benefits. However, this new distributed ML paradigm raises new risks of privacy and security issues. In this paper, we provide a survey of the emerging security and privacy risks of distributed ML from a unique perspective of information exchange levels, which are defined according to the key steps of an ML process, i.e.: i) the level of preprocessed data, ii) the level of learning models, iii) the level of extracted knowledge and, iv) the level of intermediate results. We explore and analyze the potential of threats for each information exchange level based on an overview of the current state-of-the-art attack mechanisms, and then discuss the possible defense methods against such threats. Finally, we complete the survey by providing an outlook on the challenges and possible directions for future research in this critical area.
... Among the current control methods, iterative learning control can complete the tracking task in a finite time. This method has been applied to various models of integer-order multi-agent system (IOMAS) [18][19][20]. But there is little report on the fractional-order iterative learning control (FOILC) of FOMAS. ...
This paper mainly explores the consensus control of multi-agent robot system with repetitive motion under the constraints of a leader and fixed topology. To realize the consensus control, a fractional order iterative learning control (FOILC) algorithm was designed under the mode of distributed open-closed-loop proportional-derivative alpha (PDα). The uniform convergence of the algorithm in finite time was discussed, drawing on factional calculus, graph theory, and norm theory, resulting in the convergence conditions. Theoretical analysis shows that, with the growing number of iterations, each agent can choose the appropriate gain matrix, and complete the tracking task in finite time. The effectiveness of the proposed method was verified through simulation.
... In recent years, the research on the coordinating control of multiagent systems (MASs) has become a major task in the field of control because of its application in various areas, such as formation control of unmanned aerial vehicles [1], air traffic control [2], and formation of multiple robots [3]. e consensus is an important and fundamental problem for the coordination control of MASs. ...
In this work, the consensus problem of fractional-order multiagent systems with the general linear model of fixed topology is studied. Both distributed PDα -type and Dα -type fractional-order iterative learning control (FOILC) algorithms are proposed. Here, a virtual leader is introduced to generate the desired trajectory, fixed communication topology is considered, and only a subset of followers can access the desired trajectory. The convergence conditions are proved using graph theory, fractional calculus, and λ norm theory. The theoretical analysis shows that the output of each agent completely tracks the expected trajectory in a limited time as the iteration number increases for both PDα -type and Dα -type FOILC algorithms. Extensive numerical simulations are given to demonstrate the feasibility and effectiveness.
... − y i,j,1 and max j=1,2,3,4 y d,2 − y i,j,2 . The maximum tracking errors are plotted inFigure 4. It shows that the maximum tracking errors of y1 and y2 tend to zero as the number of iterations increases with PD α -type FOILC. ...
This paper considers the leader-following consensus tracking problem of fractional-order multi-agent systems (FOMASs) that contain communication time delays. By combining the iterative learning control (ILC) approach and fractional-order calculus, a distributed PD
α
-type fractional-order iterative learning control (FOILC) and a distributed D
α
-type FOILC algorithm are proposed, respectively. Based on graph theory and λ-norm theory, the consensus problems of the proposed algorithms are discussed, and their convergence conditions are identified. The theoretical analysis demonstrates that as the number of iterations increases, all fractional-order agents with communication time delays can realize consensus exactly on the desired output trajectory by selecting suitable gain matrices of FOILC over a finite time interval. Illustrative examples are presented, on which the performances of the proposed method are evaluated.
This paper introduces three types of controllers: a PID-type iterative learning controller, an adaptive iterative learning controller, and an optimal iterative learning controller, and reviews the history and research status of initial shifts rectifying algorithms. Initial state shifts have attracted research attention because they affect both the tracking performance and system stability. This study focuses on the current common initial shifts rectifying methods and analyzes the underlying mechanism in detail. To verify the effectiveness of the presented initial shifts rectifying algorithms, we simulated those using ideal first- and second-order systems. Finally, directions for the future development of iterative learning control (ILC) and some challenging topics related to initial shifts rectifying for ILC are presented. This article aims to introduce recent developments and advances in initial shifts rectifying algorithms and discuss the directions for their further exploration.
In this study, We propose a compensated distributed adaptive learning algorithm for heterogeneous multi-agent systems with repetitive motion, where the leader’s dynamics are unknown, and the controlled system’s parameters are uncertain. The multi-agent systems are considered a kind of hybrid order nonlinear systems, which relaxes the strict requirement that all agents are of the same order in some existing work. For theoretical analyses, we design a composite energy function with virtual gain parameters to reduce the restriction that the controller gain depends on global information. Considering the stability of the controller, we introduce a smooth continuous function to improve the piecewise controller to avoid possible chattering. Theoretical analyses prove the convergence of the presented algorithm, and simulation experiments verify the effectiveness of the algorithm.
Motivated by the advancing computational capacity of distributed end-user equipment (UE), as well as the increasing concerns about sharing private data, there has been considerable recent interest in machine learning (ML) and artificial intelligence (AI) that can be processed on distributed UEs. Specifically, in this paradigm, parts of an ML process are outsourced to multiple distributed UEs. Then, the processed information is aggregated on a certain level at a central server, which turns a centralized ML process into a distributed one and brings about significant benefits. However, this new distributed ML paradigm raises new risks in terms of privacy and security issues. In this article, we provide a survey of the emerging security and privacy risks of distributed ML from a unique perspective of information exchange levels, which are defined according to the key steps of an ML process, i.e., we consider the following levels: 1) the level of preprocessed data; 2) the level of learning models; 3) the level of extracted knowledge; and 4) the level of intermediate results. We explore and analyze the potential of threats for each information exchange level based on an overview of current state-of-the-art attack mechanisms and then discuss the possible defense methods against such threats. Finally, we complete the survey by providing an outlook on the challenges and possible directions for future research in this critical area.
This article studies the human-in-the-loop fuzzy iterative learning control of leader-following consensus for unknown mixed-order nonlinear multi-agent systems. The human operator participates in the cooperative control of multi-agent systems, which indirectly affects the followers by directly controlling the leader. Moreover, the leader's input is unknown to all followers. The mixed-order multi-agent systems contain both first- and second-order agents, which include the special case of the second-order multi-agent systems. By using fuzzy logic systems to approximate unknown nonlinear dynamics, a fully distributed fuzzy iterative learning controller with time-varying coupling gain is designed. In the estimation parameters, a
-modification related to the number of iterations is designed to ensure the convergence of the closed-loop systems. Based on the new composite energy function, the exact consensus of the closed-loop systems is proved. Finally, the simulation results verify the effectiveness of the designed control algorithm.
This article introduces a new traffic control system framework, Mobile Intelligent Traffic Management System (MITCS), designed for Baku for the next generation. According to statistics, every year people lose 154 hours in traffic on average. 1.3 million people die in accidents. The system combines micro-mechanical and electrical technologies embedded system, wireless transmission, image processing, and solar module. The objectives of this study are: 1. Research and design new and multifunctional traffic controller in the box; 2. Design a cost-effective basis contribution to the communication network; 3. Use image processing methods of developing a detector of non-interfering means for control of traffic dynamics; 4. Using artificial intelligence adapt traffic dynamics and update traffic control strategies; 5. Propose a special concept for mobile intelligent traffic control Center. Finally, an experimental system consisting of Virtual Traffic Police (VTP), Status Monitor Agent (SMA) and Traffic Control Integration Module (TCIM). There will be a system highly efficient, self-organized and self-coordinated support motion control mechanism. Keywords: Transportation, artificial intelligence, information technologies.
This article focuses on global fuzzy consensus control of unknown second‐order nonlinear multi‐agent systems based on adaptive iterative learning scheme. In order to achieve global consensus, a replacement idea is introduced, where fuzzy systems are used as feedforward compensators to model unknown nonlinear dynamics relying on tracking signals. Considering that the network communication is distributed, a kind of hybrid control protocol is designed to avoid the complete dependence on the tracking signals. In addition, considering the complexity of the external environment, this article extends the above distributed protocol to the case of unknown control directions to study global consensus. Finally, the feasibility of the proposed protocols is verified by Matlab numerical simulations.
In this article, the optimal consensus problem at specified data points is considered for heterogeneous networked agents with iteration-switching topologies. A point-to-point linear data model (PTP-LDM) is proposed for heterogeneous agents to establish an iterative input-output relationship of the agents at the specified data points between two consecutive iterations. The proposed PTP-LDM is only used to facilitate the subsequent controller design and analysis. In the sequel, an iterative identification algorithm is presented to estimate the unknown parameters in the PTP-LDM. Next, an event-triggered point-to-point iterative learning control (ET-PTPILC) is proposed to achieve an optimal consensus of heterogeneous networked agents with switching topology. A Lyapunov function is designed to attain the event-triggering condition where only the control information at the specified data points is available. The controller is updated in a batch wise only when the event-triggering condition is satisfied, thus saving significant communication resources and reducing the number of the actuator updates. The convergence is proved mathematically. In addition, the results are also extended from linear discrete-time systems to nonlinear nonaffine discrete-time systems. The validity of the presented ET-PTPILC method is demonstrated through simulation studies.
In this paper, two iterative learning control methods are proposed for the different high-order systems with arbitrary initial shifts. The tracking errors caused by nonzero initial shifts are easily detected when applying conventional learning algorithms. But this defect is overcome through applying a step-bystep rectifying controller with initial initial rectifying action introduced in a small interval. It demonstrates the improvement of tracking performance and shows the robustness with respect to the stochastic initial shifts. Finally, simulation results are presented to illustrate the effectiveness of the stated algorithms.
High performance consensus tracking of networked dynamical systems working repetitively is an important class of coordination problems and it has found many applications in different areas. Recently, iterative learning control (ILC), which does not require a highly accurate model to achieve the high performance requirement, has been developed for the consensus tracking problem. Most of existing ILC algorithms consider about the tracking of a reference defined over the whole trial length, while the Point-to-Point (P2P) task where the emphasis is placed on the tracking of intermediate time instant points, has not been explored. To bridge this gap, we develop a norm optimal ILC (NOILC) algorithm for P2P consensus tracking problem that guarantees not only the monotonic convergence of consensus tracking error norm to zero, but also the convergence of input to the minimum input energy solution, which is desired in practice. Moreover, using the idea of the alternating direction method of multipliers, we develop a distributed implementation method for the proposed algorithm, allowing the resulting algorithm to be applied to large scale networked dynamical systems. Rigorous analysis of the algorithm’s properties is provided and numerical simulations are given to verify its effectiveness.
Based on the theory of cloud control systems, an intelligent transportation cyber-physical cloud control system is designed due to the problems of complex objects, big data, high demand for transmission and calculation and poor real-time control ability in the modern intelligent transportation cyber-physical network. It includes intelligent transportation edge control technology and intelligent transportation network virtualization technology. Based on the big data of intelligent traffic flow, two intelligent learning methods, deep learning and extreme learning machine, are used to train and predict the traffic flow data on the servers of the cloud control management center. The short time traffic flow and the congestion of roads are predicted accurately. Then the real-time traffic flow control strategy is obtained by intelligent optimization scheduling algorithm in the cloud. The problem of traffic flow distribution in congested roads is solved and the dynamic performance of intelligent transportation control systems can be improved.
This survey paper studies deterministic control systems that integrate three of the most active research areas during the last years: (1) online learning control systems, (2) distributed control of networked multiagent systems, and (3) hybrid dynamical systems (HDSs). The interest for these types of systems has been motivated mainly by two reasons: First, the development of cheap massive computational power and advanced communication technologies, which allows to carry out large computations in complex networked systems, and second, the recent development of a comprehensive theory for HDSs that allows to integrate continuous‐time dynamical systems and discrete‐time dynamical systems in a unified manner, thus providing a unifying modeling language for complex learning‐based control systems. In this paper, we aim to give a comprehensive survey of the current state of the art in the area of online learning control in multiagent systems, presenting an overview of the different types of problems that can be addressed, as well as the most representative control architectures found in the literature. These control architectures are modeled as HDSs, which include as special subsets continuous‐time dynamical systems and discrete‐time dynamical systems. We highlight the different advantages and limitations of the existing results as well as some interesting potential future directions and open problems.
In this paper, we investigate the perfect consensus problem for second-order linearly parameterised multi-agent systems (MAS) with imprecise communication topology structure. Takagi-Sugeno (T–S) fuzzy models are presented to describe the imprecise communication topology structure of leader-following MAS, and a distributed adaptive iterative learning control protocol is proposed with the dynamic of leader unknown to any of the agent. The proposed protocol guarantees that the follower agents can track the leader perfectly on [0,T] for the consensus problem. Under alignment condition, a sufficient condition of the consensus for closed-loop MAS is given based on Lyapunov stability theory. Finally, a numerical example and a multiple pendulum system are given to illustrate the effectiveness of the proposed algorithm.
This paper investigates the consensus problem for linear multi-agent systems from the viewpoint of two-dimensional systems when the state information of each agent is not available. Observer-based fully distributed adaptive iterative learning protocol is designed in this paper. A local observer is designed for each agent and it is shown that without using any global information about the communication graph, all agents achieve consensus perfectly for all undirected connected communication graph when the number of iterations tends to infinity. The Lyapunov-like energy function is employed to facilitate the learning protocol design and property analysis. Finally, simulation example is given to illustrate the theoretical analysis.
The concept of cloud control systems is discussed in this paper, which is an extension of networked control systems (NCSs). With the development of internet of things (IOT), the technology of NCSs has played a key role in IOT. At the same time, cloud computing is developed rapidly, which provides a perfect platform for big data processing, controller design and performance assessment. The research on cloud control systems
will give new contribution to the control theory and applications in the near future.
This paper considers the problem of iterative learning control design for linear systems with data quantization. It is assumed that the control input update signals are quantized before they are transmitted to the iterative learning controller. A logarithmic quantizer is used to decode the signal with a number of quantization levels. Then, a 2-D Roesser model is established to describe the entire dynamics of the iterative learning control (ILC) system. By using the sector bound method, a sufficient asymptotic stability condition for such a 2-D system is established and then the ILC design is given simultaneously. The result is also extended to more general cases where the system matrices contain uncertain parameters. The effectiveness of the proposed method is illustrated by a numerical example. © 2016 Chinese Automatic Control Society and John Wiley & Sons Australia, Ltd.
This paper investigates the distributed coordination problem for leader-follower multi-agent systems with secondorder nonlinear dynamics by using adaptive iterative learning control. It is assumed that the state information of the leader is only available to a portion of the follower agents and the bounded input of the leader is unavailable to any follower agent. Without using any global information, a fully distributed adaptive iterative learning protocol with distributed adaptive learning laws for the control gains is designed in this article, under which consensus is reached for all undirected connected communication graph. Finally, the simulation example is given to illustrate the theoretical analysis.
This paper proposes a finite time frequency controller that synchronizes the microglia frequency to the nominal frequency and shares the active power among distributed generators (DG) based on their active power ratings. The finite-time control accelerates the synchronization speed and provides the synchronization for microgrid frequency and DG active powers in a finite period of time. In addition, the proposed control is distributed; i.e., each DG only requires its own information and the information of its neighbors on the communication network graph. The efficacy of the proposed finite-time frequency control subsequent to islanding process and load changes is verified for an islanded microgrid test system.
In this paper, the problem of iterative learning control (ILC) for discrete-time systems with quantized output measurements is considered. Here, a logarithmic quantizer is introduced and an ILC scheme is constructed by using output signals with only a finite number of quantization levels. By using sector bound method to deal with the quantization error, a learning condition of ILC that guarantees the convergence of tracking error is derived through rigorous analysis. It is shown that the convergence condition is determined by quantization level, and the tracking error converges to a bound depending on quantization density. Finally, an illustrative example is presented to demonstrate the theoretical results.
In this paper, leader–follower coordination problems of a kind of heterogeneous multi-agent systems are studied by applying iterative learning control (ILC) scheme in a repeatable control environment. The heterogeneous multi-agent systems are composed of first-order and second-order dynamics in two aspects. The leader is assumed to have second-order dynamics and the trajectories of the leader are only accessible to a subset of the followers. To overcome the strict identical initial condition commonly used in ILC, the distributed initial state learning controller for each follower is designed, thus each follower agent can take arbitrary initial state. Distributed iterative learning protocols guarantee that all follower agents can achieve perfect tracking consensus for both fixed and switching communication topologies, respectively. In addition, the proposed scheme is also extended to achieve formation control for heterogeneous multi-agent system. Finally, simulation examples are given to illustrate the effectiveness of the proposed methods in this article.
The problem of cooperative guidance of multiple missiles attacking a stationary target, which can be achieved by consensus of the times-to-go is illustrated in this study. First, the finite-time cooperative guidance (FTCG) law is put forwarded to realise rapid and precise consensus of the times-to-go of all the missiles. Then, the FTCG law is modified to accommodate the condition in the presence of acceleration saturation constraint, and global ultimately finite-time consensus of times-to-go is also guaranteed. Finally, in order to adapt the realistic situation that each missile can only employ neighbour-to-neighbour communication, the distributed FTCG law is proposed. This guidance law adopts the sequential method, and can also cope with acceleration saturation constraint. The simulation results based on current control scheme and the comparison with the previous method demonstrate the effectiveness of the proposed laws.
In this study, the problem of iterative learning control (ILC) for discrete-time systems with quantised output measurements is considered. Here, a logarithmic quantiser is introduced and an ILC scheme is constructed by using output signals with only a finite number of quantisation levels. By using sector bound method to deal with the quantisation error, a learning condition of ILC that guarantees the convergence of tracking error is derived through rigorous analysis. It is shown that the convergence condition is determined by quantisation level, and the tracking error converges to a bound depending on quantisation density. Furthermore, the extension from linear systems to non-linear systems is also addressed. Finally, two illustrative examples are presented to demonstrate the theoretical results for both linear and non-linear systems.
This study discusses the asymptotic consensus problem and finite-time leader-following consensus problem of second-order non-linear multi-agent systems (MASs) with directed communication topology. On the basis of the sliding mode control theory, a new distributed asymptotic consensus controller is proposed to ensure that the consensus of MAS can be reached as time goes to infinity. Another finite-time consensus control algorithm is also proposed based on terminal sliding mode control. The finite-time consensus controller can force the states of MAS to achieve the designed terminal sliding mode surface in finite time and maintain on it. The authors also can prove the consensus of MAS can be obtained in finite time on the terminal sliding mode surface if the directed topology has a directed spanning tree. Simulations are given to illustrate the effectiveness of the proposed approaches.
This paper investigates the distributed coordination problem for leader-follower multi-agent systems with second-order nonlinear dynamics by using adaptive iterative learning control. It is assumed that the state information of the leader is only available to a portion of the follower agents and the bounded input of the leader is unavailable to any follower agent. Without using any global information, a fully distributed adaptive iterative learning protocol with distributed adaptive learning laws for the control gains is designed in this article, under which consensus is reached for all undirected connected communication graph. Furthermore, as an extension of the former result, the formation problem is studied. Finally, simulation examples are given to illustrate the theoretical analysis.
In this paper, the adaptive fuzzy iterative learning control scheme is proposed for coordination problems of Mth order (M ≥ 2) distributed multi-agent systems. Every follower agent has a higher order integrator with unknown nonlinear dynamics and input disturbance. The dynamics of the leader are a higher order nonlinear systems and only available to a portion of the follower agents. With distributed initial state learning, the unified distributed protocols combined time-domain and iteration-domain adaptive laws guarantee that the follower agents track the leader uniformly on [0, T]. Then, the proposed algorithm extends to achieve the formation control. A numerical example and a multiple robotic system are provided to demonstrate the performance of the proposed approach.
This paper is devoted to the robust finite-time output consensus problems of multi-agent systems under directed graphs, where all agents and their communication topologies are subject to interval uncertainties. Distributed protocols are constructed by using iterative learning control (ILC) algorithms, where information is exchanged only at the end of one iteration and learning is used to update the control inputs after each iteration. It is proved that under ILC-based protocols, the finite-time consensus can be achieved with an increasing number of iterations if the communication network of agents is guaranteed to have a spanning tree. Moreover, if the information of any desired terminal output is available to a portion (not necessarily all) of the agents, then the consensus output that all agents finally reach can be enabled to be the desired terminal output. It is also proved that for all ILC-based protocols, gain selections can be provided in terms of bound values, and consensus conditions can be developed associated with bound matrices. Simulation results are given to demonstrate the effectiveness of our theoretical results.
This paper aims to address finite-time consensus problems for multi-agent systems under the iterative learning control framework. Distributed iterative learning protocols are presented, which adopt the terminal laws to update the control input and are offline feedforward design approaches. It is shown that iterative learning protocols can guarantee all agents in a directed graph to reach the finite-time consensus. Furthermore, the multi-agent systems can be enabled to achieve a finite-time consensus at any desired terminal state/output if iterative learning protocols can be improved by introducing the desired terminal state/output to a portion of agents. Simulation results show that iterative learning protocols can effectively accomplish finite-time consensus objectives for both first-order and higher order multi-agent systems.
In this paper, a novel neural network based terminal iterative learning control method is proposed for a class of uncertain nonlinear non-affine systems to track run-varying reference point with initial state variance. In this new control scheme, the non-affine terminal dynamics are converted affine, and the unrealisable recurrent network is simplified into realisable static network. As a result, the effect of initial state and control signal on terminal output can be estimated by neural network. With this estimation, the proposed control scheme can drive nonlinear non-affine systems to track run-varying reference point in the presence of initial state variance. Stability and convergence of this approach are proven, and numerical simulation results are provided to verify its effectiveness.
Repeated practice is one of the most effective methods in improving the performance of coordination control tasks for groups of individuals, such as marching band, soldier (tank or warcraft) formation, and unmanned aerial vehicle flying queue. The key objective of this paper is to give a theoretical explanation for this observed behavior by considering a class of coordination learning problems for groups of mobile agents. To be specific, the agents are considered to preserve the desired relative formations between each other through a learning process, for which iterative rules are applied to construct distributed algorithms based on the relative information between each agent and its neighbors. Convergence results are derived by combining the graph theory based method and the Lyapunov analysis, which can address coordination learning problems for multi-agent systems both with and without a reference as the prior knowledge. In addition, numerical simulation results are provided to demonstrate the coordination learning performance for groups of mobile agents.
In this paper, input–output feedback linearization is used to design distributed controls for multi-agent systems with nonlinear and heterogeneous non-identical dynamics. Using feedback linearization, the nonlinear and heterogeneous dynamics of agents are transformed to identical linear dynamics and non-identical internal dynamics. Based on the dependence of agent outputs on agent inputs, feedback linearization may lead to a first-order or high-order tracking synchronization problem. The controller for each agent is designed to be fully distributed such that each agent only requires its own information and the information of its neighbors. The effectiveness of the proposed control protocols are verified by simulation on a microgrid test system.
This paper investigates the average-consensus problem of first-order discrete-time multi-agent networks in uncertain communication environments. Each agent can only use its own and neighbors' information to design its control input. To attenuate the communication noises, a distributed stochastic approximation type protocol is used. By using probability limit theory and algebraic graph theory, consensus conditions for this kind of protocols are obtained: (A) For the case of fixed topologies, a necessary and sufficient condition for mean square average-consensus is given, which is also sufficient for almost sure consensus. (B) For the case of time-varying topologies, sufficient conditions for mean square average-consensus and almost sure consensus are given, respectively. Especially, if the network switches between jointly-containing-spanning-tree, instantaneously balanced graphs, then the designed protocol can guarantee that each individual state converges, both almost surely and in mean square, to a common random variable, whose expectation is right the average of the initial states of the whole system, and whose variance describes the static maximum mean square error between each individual state and the average of the initial states of the whole system.
This paper presents a robust design approach for terminal iterative learning control (TILC). This robust design uses the H∞ mixed-sensitivity technique. An industrial application is described where TILC is used to control the reheat phase of plastic sheets in a thermoforming oven. The TILC adjusts the heater temperature setpoints such that, at the end of the reheat cycle, the surface temperature map of the plastic sheet will converge to the desired one. Simulation results are included to show the effectiveness of the control law.
This article surveyed the major results in iterative learning control (ILC) analysis and design over the past two decades. Problems in stability, performance, learning transient behavior, and robustness were discussed along with four design techniques that have emerged as among the most popular. The content of this survey was selected to provide the reader with a broad perspective of the important ideas, potential, and limitations of ILC. Indeed, the maturing field of ILC includes many results and learning algorithms beyond the scope of this survey. Though beginning its third decade of active research, the field of ILC shows no sign of slowing down.
Arbitrary high precision output tracking is one of the most desirable control objectives found in industrial applications regardless of measurement errors. The main purpose of this paper is to supply to the iterative learning control (ILC) designer guidelines to select the corresponding learning gain in order to achieve this control objective. For example, if certain conditions are met, then it is necessary for the learning gain to converge to zero in the learning iterative domain. In particular, this paper presents necessary and sufficient conditions for boundedness of trajectories and uniform tracking in presence of measurement noise and a class of random reinitialization errors for a simple ILC algorithm. The system under consideration is a class of discrete-time affine nonlinear systems with arbitrary relative degree and arbitrary number of system inputs and outputs. The state function does not need to satisfy a Lipschitz condition. This work also provides a recursive algorithm that generates the appropriate learning gain functions that meet the arbitrary high precision output tracking objective. The resulting tracking output error is shown to converge to zero at a rate inversely proportional to square root of the number of learning iterations in presence of measurement noise and a class of reinitialization errors. Two illustrative numerical examples are presented.
Iterative Learning Control (ILC) improves the tracking accuracy of systems that repetitively perform the same task. This paper considers model-based ILC for linear time-varying (LTV) systems. The applied feedforward iteratively minimises a quadratic norm of the feedforward update and the error in the next iteration as predicted by the model. The optimal feedforward update can be derived straightforwardly using a matrix description of the system dynamics. However, the implementation of the resulting matrix equation is demanding in terms of computation time and memory. In this paper it is shown that an efficient algorithm can be derived directly from the matrix equation using the associated state-equations.The ILC algorithm is applied to an industrial robot. The configuration dependent robot dynamics can be approximated as LTV for small tracking errors from the large-scale motion along the desired trajectory. It is shown that a substantial reduction of the tracking error at the robot’s tip can be realised by ILC using an LTV model of the robot dynamics and the same reduction cannot be accomplished using an LTI model that ignores the variation of the robot dynamics along the trajectory.
This paper deals with the stability analysis of discrete iterative learning control (ILC) by developing a two-dimensional (2-D) approach under the Roesser systems framework. The system under consideration is a class of multiple-input multiple-output (MIMO), linear time-varying (LTV) systems. Using a type of two-gain ILC, it is shown that once the theory is established for the discrete-time-varying 2-D Roesser systems, a necessary and sufficient condition for the stability of ILC process can be determined directly. Numerical simulation is included to verify the theoretical results.
Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society
This paper proposes an iterative learning control (ILC) scheme to ensure trajectory-keeping in satellite formation flying. Since satellites rotate the earth periodically, position-dependent disturbances can be considered time-periodic disturbances. This observation motivates the idea of repetitively compensating for external disturbances such as solar radiation, magnetic field, air drag, and gravity forces in an iterative, orbit-to-orbit manner. It is shown that robust ILC can be effectively utilized for satellite trajectory tracking, thus enabling time-variant formation flying between the leader- and follower-satellites. The validity of the results is illustrated through computational simulations. Copyright © 2009 John Wiley & Sons, Ltd.
This paper considers finite-time χ-consensus problem for a multi-agent system with first-order individual dynamics and switching
interaction topologies. Several distributed finite-time consensus rules are constructed for multi-agent dynamics in a unified
way with the help of Lyapunov function and graph theory as well as homogeneity. Time-invariant non-smooth forms of finite-time
neighbor-based controllers are proposed and a numerical example is shown for illustration.
Key wordsχ-consensus-distributed control-multi-agent networks-non-smoothness-switching graphs
This note is concerned with the robust discrete-time iterative learning control (ILC) design for nonlinear systems with varying initial state shifts. A two-gain ILC law is considered using a 2D analysis approach. Sufficient conditions are derived to guarantee both convergence of the learning process for fixed initial condition and boundedness of the tracking error for variable initial condition. It is shown that the error data with anticipation in time can well handle the varying initial state shifts in discrete-time ILC.
This study is devoted to the problem of robust iterative learning control (ILC) for time-delay systems (TDS) when the plants are subject to random iteration-varying uncertainties. Using the frequency-domain approach, an ILC scheme is considered within the Smith predictor-based feedback configuration. It shows that if the well-known robust performance condition is satisfied, then an updating law can be obtained directly to guarantee that the ILC process converges in the sense of expectation. In particular, if the unit function is selected as the performance weight, then the expected tracking error converges monotonically to zero as a function of iteration. Two numerical examples are presented to illustrate the effectiveness of the Smith predictor-based ILC.
Here the authors concerned with robust iterative learning control (ILC) for uncertain time-delay systems. They demonstrate that the design of a robust ILC is straightforward based on a performance index for the error system. The ILC algorithms under consideration are rather simple. They show that after the two-dimensional analysis of ILC, a Lyapunov-like approach can be used to directly obtain a stable algorithm that achieves monotonic convergence of the control input error. Sufficient stability conditions are provided in terms of linear matrix inequalities, which can determine learning gains as well. They also show that the Lyapunov-like approach can be applied to design robust ILC for uncertain systems with time-varying delay or multiple time delays. Numerical simulation results are presented to illustrate the effectiveness of the proposed ILC approach.
In this note, we discuss finite-time state consensus problems for multi-agent systems and present one framework for constructing effective distributed protocols, which are continuous state feedbacks. By employing the theory of finite-time stability, we investigate both the bidirectional interaction case and the unidirectional interaction case, and prove that if the sum of time intervals, in which the interaction topology is connected, is sufficiently large, the proposed protocols will solve the finite-time consensus problems.
This paper employs iterative learning control scheme to generate a sequence of control signals for multi-agent formation control. It is assumed that individual agent of a group of multi-agents is governed by nonlinear dynamics, which could be known in part; in such case, we would like to find control sequences of individual agents such that they form a desired formation with respect to other agents, from initial starting points to final stop points. That is, we would like to ensure that the multi-agents form relative desired states with respect to other agents along the desired trajectory. The algorithm established in this paper can be used to find a control sequence of multi-agent systems for keeping relative formation, in off-line tuning manner. The utility of the algorithm established in this paper can be therefore used for finding optimal control strategy of nonlinear dynamic systems with partially available system information.
This paper introduces the normalized and signed gradient dynamical systems associated with a differentiable function. Extending recent results on nonsmooth stability analysis, we characterize their asymptotic convergence properties and identify conditions that guarantee finite-time convergence. We discuss the application of the results to consensus problems in multi-agent systems and show how the proposed nonsmooth gradient flows achieve consensus in finite time. (c) 2006 Elsevier Ltd. All rights reserved.
The consensus problem of second-order multi-agent systems with diverse input delays is investigated. Based on the frequency-domain analysis, decentralized consensus conditions are obtained for the multi-agent system with symmetric coupling weights. Then, the robustness of the symmetric system with asymmetric perturbation is studied. A bound of the largest singular value of the perturbation matrix is obtained as the robust consensus condition. Simulation examples illustrate the design procedure of consensus protocols and validate the correctness of the results.
This paper addresses the initial shift problem in iterative learning control with system relative degree. The tracking error caused by nonzero initial shift is detected when applying a conventional learning algorithm. Finite initial rectifying action is introduced in the learning algorithm and is shown effective in the improvement of tracking performance, in particular robustness with respect to variable initial shifts. The uniform convergence of the output trajectory to a desired one jointed smoothly with a specified transient trajectory from the starting position is ensured in the presence of fixed initial shift.
A special type of iterative learning control (ILC) problem is considered. Due to the insufficient measurement capability in many real control problems such as Rapid Thermal Processing (RTP), it may happen that only the terminal output tracking error instead of the whole output trajectory tracking error is available. In the RTP chemical vapor deposition (CVD) of wafer fab. industry, the ultimate control objective is to control the deposition thickness (DT) at the end of the RTP cycle. The control profile for the next operation cycle has to be updated using the terminal DT tracking error alone. A revised ILC method is proposed to address this terminal output tracking problem. By parameterizing the control profile with a piecewise continuous functional basis, the parameters are updated by a high-order updating scheme. A convergence condition is obtained for a class of uncertain discrete-time time-varying linear systems including the RTPCVD system as the subset. Simulation results for an RTPCVD thickness control problem are presented to demonstrate the effectiveness of the proposed iterative learning scheme.
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 article deals with the initial shift problem of robust iterative learning control (ILC) for uncertain continuous-time systems. Two ILC laws are considered by the two-dimensional (2-D) analysis approach. It is shown that a necessary and sufficient convergence condition can be directly derived using the theory of 2-D systems. It is also shown that if the system parameters are subject to polytopic-type uncertainties, this convergence condition can induce a sufficient condition for the robust ILC convergence. Furthermore, the 2-D analysis approach can be extended to address the initial shift problem of robust ILC for multiple-input–multiple-output, uncertain time-delay systems. Two numerical simulation examples are provided to illustrate the theoretical results.
Without assuming that the interaction diagraph is strongly connected or contains a directed spanning tree, this paper studies the second-order leader-following consensus problem of nonlinear multi-agent systems with general network topologies. Based on graph theory, matrix theory, and LaSalle’s invariance principle, a pinning control algorithm is proposed to achieve leader-following consensus in a network of agents with nonlinear second-order dynamics. Furthermore, a pinning consensus protocol is developed for coupled double-integrators with a constant reference velocity. In particular, this paper addresses what kind of agents and how many agents should be pinned, and establishes some sufficient conditions to guarantee that all agents asymptotically follow the virtual leader. Numerical simulations are given to verify the theoretical analysis.
The disturbance properties of high order iterative learning control (ILC) algorithms are considered. An error equation is formulated, and using statistical models of the load and measurement disturbances an equation for the covariance matrix of the control error vector is derived. The results are exemplified by analytic derivation of the covariance matrix for a second order ILC algorithm.
Distributed finite-time attitude containment control for multiple rigid bodies is addressed in this paper. When there exist multiple stationary leaders, we propose a model-independent control law to guarantee that the attitudes of the followers converge to the stationary convex hull formed by those of the leaders in finite time by using both the one-hop and two-hop neighbors’ information. We also discuss the special case of a single stationary leader and propose a control law using only the one-hop neighbors’ information to guarantee cooperative attitude regulation in finite time. When there exist multiple dynamic leaders, a distributed sliding-mode estimator and a non-singular sliding surface were given to guarantee that the attitudes and angular velocities of the followers converge, respectively, to the dynamic convex hull formed by those of the leaders in finite time. We also explicitly show the finite settling time.
This paper studies the consensus problem of multi-agent systems with nonuniform time-delays and dynamically changing topologies. A linear consensus protocol is introduced to realize local control strategies for these second-order discrete-time agents. By model transformations and applying the properties of nonnegative matrices, sufficient conditions are derived for state consensus of the systems. It is shown that arbitrary bounded time-delays can safely be tolerated, even though the communication structures between agents dynamically change over time and the corresponding directed graphs may not have spanning trees. Finally, a numerical example is included to illustrate the obtained results.
Finite-time stability is defined for equilibria of continuous but non-Lipschitzian autonomous systems. Continuity, Lipschitz continuity, and Holder continuity of the settling-time function are studied and illustrated with several examples. Lyapunov and converse Lyapunov results involving scalar differential inequalities are given for finite-time stability. It is shown that the regularity properties of the Lyapunov function and those of the settling-time function are related. Consequently, converse Lyapunov results can only assure the existence of continuous Lyapunov functions. Finally, the sensitivity of finite-time-stable systems to perturbations is investigated.
A novel feedback control method for robotic manipulators with random communication delays by combining the optimal P-type iterative learning control (ILC) idea with a minimum tracking error entropy control strategy is presented. The control design is formulated as an optimisation problem with a proper performance index and a constraint. In specific, the performance index implies the idea of the minimum entropy control of the closed-loop tracking error. The convergence in the mean-square sense has been analysed for all the signals in the closed-loop system. The convergence condition of such a tracking error under ILC framework is treated as the constraint condition which is satisfied in the optimisation process. It has been shown that the numerical optimal solution per iteration can be obtained by using the well-known particle swarm optimisation techniques. Simulation results are provided to show the effectiveness of the proposed approach.
We examine the consensus problem for a group of agents that communicate via a stochastic information network. Communication among agents is modeled as a weighted directed random graph that switches periodically. The existence of any edge is probabilistic and independent from the existence of any other edge. We further allow each edge to be weighted differently. Sufficient conditions for asymptotic almost sure consensus are presented for the case of positive weights and for the case of arbitrary weights.
This note considers the problem of information consensus among multiple agents in the presence of limited and unreliable information exchange with dynamically changing interaction topologies. Both discrete and continuous update schemes are proposed for information consensus. This note shows that information consensus under dynamically changing interaction topologies can be achieved asymptotically if the union of the directed interaction graphs have a spanning tree frequently enough as the system evolves.
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.
Stereo vision-based formation control of mobile robots using iterative learning
- X Chen
- Y Jia
Chen, X., Jia, Y.: 'Stereo vision-based formation control of mobile robots using iterative learning'. Proc. Int. Conf. on Humanized Systems, Kyoto, Japan, September 2010, pp. 62–67