Consensus seeking via iterative learning for multi‐agent systems with switching topologies and communication time‐delays

This paper deals with the high‐precision consensus seeking problem of multi‐agent systems when they are subject to switching topologies and varying communication time‐delays. By combining the iterative learning control (ILC) approach, a distributed consensus seeking algorithm is presented based on only the relative information between every agent and its local (or nearest) neighbors. All agents can be enabled to achieve consensus exactly on a common output trajectory over a finite time interval. Furthermore, conditions are proposed to guarantee both exponential convergence and monotonic convergence for the resulting ILC processes of multi‐agent consensus systems. In particular, the linear matrix inequality technique is employed to formulate the established convergence conditions, which can directly give formulas for the gain matrix design. An illustrative example is included to validate the effectiveness of the proposed ILC‐motivated consensus seeking algorithm. Copyright © 2016 John Wiley & Sons, Ltd.     

Robust and nonfragile consensus of positive multiagent systems via observer‐based output‐feedback protocols

This article investigates the consensus problem for positive multiagent systems via an observer‐based dynamic output‐feedback protocol. The dynamics of the agents are modeled by linear positive systems and the communication topology of the agents is expressed by an undirected connected graph. For the consensus problem, the nominal case is studied under the semidefinite programming framework while the robust and nonfragile cases are investigated under the linear programming framework. It is required that the distributed state‐feedback controller and observer gains should be structured to preserve the positivity of multiagent systems. Necessary and/or sufficient conditions for the analysis of consensus are obtained by using positive systems theory and graph theory. For the nominal case, necessary and sufficient conditions for the codesign of state‐feedback controller and observer of consensus are derived in terms of matrix inequalities. Sufficient conditions for the robust and nonfragile consensus designs are derived and the codesign of state‐feedback controller and observer can be obtained in terms of solving a set of linear programs. Numerical simulations are provided to show the effectiveness and applicability of the theoretical results and algorithms.     

Observer‐Based Consensus Tracking for Nonlinear Multi‐Agent Systems With Intermittent Communications

This paper addresses the observer‐based consensus tracking problem of multi‐agent systems with intermittent communications. The agent dynamics are modeled as general linear systems with Lipschitz nonlinearity. Under the assumption that each agent can intermittently share its relative output with neighbors, a class of an observer‐type protocol is proposed, and the consensus tracking problem can be converted further into the stability problem of the nonlinear switching systems. Using a combined tool from M matrix theory, switching theory and the averaging approach, a multi‐step algorithm is presented to construct the observer gains and protocol parameters, and the sufficient criteria established not only can ensure the state estimates convergence to the real values but also can guarantee the follower states synchronize to those of the leader. The obtained results reveal the relationships among the communication rate, the convergence rate, and the dwell time of switching topologies. Finally, the theoretical findings are validated by a numerical example.     

Consensus of networked multi-agent systems with communication delays based on the networked predictive control scheme

The consensus problem of discrete-time networked multi-agent systems (NMASs) with a communication delay is investigated in this article, where the dynamics of agents described by discrete-time linear time-invariant systems can be either uniform or non-uniform. For the NMASs with a directed topology and constant delay, a novel protocol based on the networked predictive control scheme is proposed to compensate for communication delay actively. Using algebraic graph theories and matrix theories, necessary and/or sufficient conditions of achieving consensus are obtained, which indicates that, under the proposed protocol, the consensus is independent of the network delay and only dominated by agents' dynamics and communication topology. Meanwhile, the protocol design and consensus analysis are also presented in the case of no network delay. Simulation results are further presented to demonstrate the effectiveness of theoretical results.     

Consensus Problem with a Reference State for Fractional‐Order Multi‐Agent Systems

In this paper, the consensus problem of fractional‐order multi‐agent systems with a reference state is studied under fixed directed communication graph. At the beginning, the convergence speeds of fractional‐order multi‐agent systems are investigated based on the Mittag‐Leffler function. Then, a common consensus control law and a consensus control law based on error predictor are proposed, and it is shown that the consensus tracking can be achieved using the above control laws when a communication graph has a directed spanning tree. Finally, the convergence speeds of fractional‐order systems are compared, and it is discovered that the convergence of systems is faster using the control law based on error predictor than using the common one.     

单向通信拓扑领航者动态未知线性多智能体系统的协同迭代学习控制（英文）

This paper considers the cooperative tracking of linear multi-agent systems with a dynamic leader whose input information is unavailable to any followers. Cooperative iterative learning controllers, based on the relative state information of neighboring agents, are proposed for tracking the dynamic leader over directed communication topologies. Stability and convergence of the proposed controllers are established using Lyapunov-Krasovskii functionals. Furthermore, this result is extended to the output feedback case where only the output information of each agent can be obtained. A local observer is constructed to estimate the unmeasurable states. Then, cooperative iterative learning controllers, based on the relative observed states of neighboring agents,are devised. For both cases, it is shown that the multi-agent systems whose communication topologies contain a spanning tree can reach synchronization with the dynamic leader, and meanwhile identify the unknown input of the dynamic leader using distributed iterative learning laws. An illustrative example is provided to verify the proposed control schemes.     

单向通信拓扑领航者动态未知线性多智能体系统的协同迭代学习控制

研究单向通信拓扑领航者动态未知线性多智能体系统的协同跟踪问题.基于邻居的相对状态信息,设计了分布式迭代学习控制律实现对领航者的协同跟踪控制,采用Lyapunov-Krasovskii函数分析闭环系统的稳定性与收敛性.进而,将状态反馈结论拓展到输出反馈,通过构造局部观测器估计不可量测的状态信息,采用估计的相对状态信息设计了分布式迭代学习控制器.对于以上两种情形,多智能体系统在通讯拓扑含有生成树的条件下能够实现与领航者的状态同步,同时,所设计的分布式迭代学习律能够对领航者未知输入进行精确估计.仿真实例验证了所提方法的有效性.     

Leader‐following control for multiple inertial agents

This paper investigates distributed controller design problem for a leader‐follower network in the presence of communication delays. Two main contributions are made in this work. First, the second‐order controlled consensus scheme for the weakly connected communication graph topology is proposed. A necessary and sufficient condition is given under which the exponential consensus is achieved. Meanwhile, the relationship among the agents' inertias, the allowable delay bound, the communication topology, the consensus convergence rate, and the control gains is unveiled. Second, the robustness performances of the distributed control scheme with respect to the communication failures and delays are provided. It is shown that if the communication failure rate and the topology switching frequency, respectively, satisfy the given bounds, the exponential second‐order controlled consensus can be achieved under a bounded delay. Numerical examples are given to illustrate the theoretical results. Copyright © 2010 John Wiley & Sons, Ltd.     

Fixed‐time output‐feedback consensus tracking control for second‐order multiagent systems

This paper is concerned with the problem of fixed‐time consensus tracking control for a class of second‐order multiagent systems under an undirected communication graph. A distributed output‐feedback fixed‐time consensus tracking control scheme is proposed to make the states of all individual agents simultaneously track a time‐varying reference state even when the reference state is available only to a subset of the group members and only output measurements are available for feedback. Homogeneous Lyapunov function and homogeneity property are employed to show that the control scheme can guarantee the consensus tracking errors converging the origin in finite time which is bounded by a fixed constant independent of initial conditions. Numerical simulations are carried out to demonstrate the effectiveness of the proposed control law.     

Coordination of discrete‐time multi‐agent systems via relative output feedback

This paper investigates the joint effects of agent dynamic and network topology on the consensusability of linear discrete‐time multi‐agent systems via relative output feedback. An observer‐based distributed control protocol is proposed. A necessary and sufficient condition for consensusability under this control protocol is given, which explicitly reveals how the intrinsic entropy rate of the agent dynamic and the eigenratio of the undirected communication graph affect consensusability. As a special case, multi‐agent systems with discrete‐time double integrator dynamics are discussed where a simple control protocol directly using two‐step relative position feedback is provided to reach a consensus. Finally, the result is extended to solve the formation and formation‐based tracking problems. The theoretical results are illustrated by simulations. Copyright © 2010 John Wiley & Sons, Ltd.     

Design of a class of nonlinear consensus protocols for multi‐agent systems

This paper investigates the consensus problem for multi‐agent systems and presents a class of nonlinear consensus protocols. First, we reveal some structure property of the corresponding Laplacian matrix by decomposing the interaction graph into strongly connected components. Then, by means of the input‐to‐state stability and algebraic graph theory, we propose a framework to prove consensus for multi‐agent systems with nonlinear protocols. In particular, we prove that consensus can be always reached in systems of single‐integrator agents with a directed communication topology containing a spanning tree, provided the nonlinear protocol is an odd and increasing function. The nonlinear consensus protocols proposed in this paper include the classical linear consensus protocol as a special case, and may have a wide range of applications, including consensus with faster convergence rates and with bounded control inputs. Copyright © 2012 John Wiley & Sons, Ltd.     

Event‐triggered output consensus for heterogeneous multiagent systems with fixed and switching directed topologies

This paper studies the event‐triggered output consensus problem of heterogeneous linear multiagent systems characterized via fixed and switching directed graphs. With proper state‐dependent triggering functions, two new event‐triggered output consensus control schemes are proposed for each agent to achieve consensus. Notably, under the proposed control protocols, continuous communication among agents is not required in both controllers updating and triggering threshold detection, which means being completely continuous communication free. The communication instances are reduced significantly, and the periodic or high‐frequency communication is restrained. It is also ensured that events cannot be triggered infinitely in finite time (ie, the Zeno behavior is elegantly avoided). Meanwhile, the simulation examples are given to illustrate the theoretical analysis.     

Output consensus for heterogeneous multiagent systems with Markovian switching network topologies

This paper investigates the output consensus problem of heterogeneous continuous‐time multiagent systems under randomly switching communication topologies. The switching mechanism is governed by a time‐homogeneous Markov process, whose states correspond to all possible communication topologies among agents. A novel dynamic consensus controller is proposed. The controller gains are designed based on the information of the expectation graph and the solutions to regulator equations. Furthermore, a necessary and sufficient condition is presented for output consensus of the controlled multiagent system in mean square sense. Finally, a simulation example is provided to corroborate the effectiveness of the proposed controller.     

Internal model approach to cooperative robust output regulation for linear uncertain time‐delay multiagent systems

In this paper, we study the cooperative robust output regulation problem for linear uncertain multiagent systems with both communication delay and input delay by the distributed internal model approach. The problem includes the leader‐following consensus problem of linear multiagent systems with time delay as a special case. We first generalize the internal model design method to systems with both communication delay and input delay. Then, under a set of standard assumptions, we have obtained the solution to the problem via both the state feedback control law and the output feedback control law. In contrast to the existing results, our results apply to general linear uncertain multiagent systems, accommodate a large class of leader signals, and achieve asymptotic tracking and disturbance rejection at the same time.     

Weighted average prediction for improving consensus performance of second-order delayed multi-agent systems

In this paper, the weighted average prediction (WAP) is introduced into the existing consensus protocol for simultaneously improving the robustness to communication delay and the convergence speed of achieving the consensus. The frequency-domain analysis and algebra graph theory are employed to derive the necessary and sufficient condition guaranteeing the second-order delayed multi-agent systems applying the WAP-based consensus protocol to achieve the stationary consensus. It is proved that introducing the WAP with the proper length into the existing consensus protocol can improve the robustness against communication delay. Also, we prove that for two kinds of second-order delayed multi-agent systems: 1) the IR-ones with communication delay approaching zero and 2) the ones with communication delay approaching the maximum delay, introducing the WAP with the proper length into the existing consensus protocol can accelerate the convergence speed of achieving the stationary consensus.     

Bipartite tracking of homogeneous and heterogeneous linear multi-agent systems

In this paper, we consider bipartite tracking of linear multi-agent systems with a leader. Both homogeneous and heterogeneous systems are investigated. The communication between agents is modelled by a directed signed graph, where the negative (positive) edges represent the antagonistic (cooperative) interactions among agents. Linear Quadratic Regulator (LQR)-based approach is used to derive the distributed protocol for the follower agent to achieve bipartite tracking of the leader. It is shown that solving the bipartite tracking problem over the structurally balanced signed graph is equivalent to solving the cooperative tracking problem over a corresponding graph with nonnegative edge weights. This bridges the gap between the newly raised bipartite tracking problem and the well-studied cooperative tracking problem. Three novel control protocols are proposed for both cooperative and bipartite output tracking of heterogeneous linear multi-agent systems. Numerical examples are given to show the effectiveness of our control protocols.     

Semi‐global leader‐following consensus of multiple linear systems with position and rate limited actuators

This paper studies the semi‐global leader‐following consensus problem for a group of linear systems in the presence of both actuator position and rate saturation. Each follower agent in the group is described by a general linear system subject to simultaneous actuator position and rate saturation. For each follower agent, we construct both a linear state feedback control law and a linear output feedback control law by using low gain approach. We show that semi‐global leader‐following consensus can be achieved by using these control laws when the communication topology among follower agents is a connected undirected graph, and the leader is a neighbor of at least one follower. Simulation results illustrate the theoretical results. Copyright © 2014 John Wiley & Sons, Ltd.     

Semi‐global output consensus of a group of linear systems in the presence of external disturbances and actuator saturation: An output regulation approach

This paper studies the problem of semi‐global leader‐following output consensus of a multi‐agent system. The output of each follower agent in the system, described by a same general linear system subject to external disturbances and actuator saturation, is to track the output of the leader, described by a linear system, which also generates disturbances as the exosystem does in the classical output regulation problem. Conditions on the agent dynamics are identified, under which a low‐gain feedback‐based linear state‐control algorithm is constructed for each follower agent such that the output consensus is achieved when the communication topology among the agents is a digraph containing no loop, and the leader is reachable from any follower agent. We also extend the results to the non‐identical disturbance case. In this case, conditions based on both the agent dynamics and the communication topology are identified, under which a low‐gain feedback‐based linear state‐control algorithm is constructed for each follower agent such that the leader‐following output consensus is achieved when the communication topology among the follower agents is a strongly connected and detailed balanced digraph, and the leader is a neighbor of at least one follower. In addition, under some further conditions on the agent dynamics, the control algorithm is adapted so as to achieve semi‐global leader‐following output consensus for a jointly connected undirected graph and the leader reachable from at least one follower. Copyright © 2015 John Wiley & Sons, Ltd.     

Exponential synchronization of nonlinear multi‐agent systems with time delays and impulsive disturbances

The problem of cooperative synchronization of nonlinear multi‐agent systems with time delays is investigated in this paper. Compared with the existing works about synchronization (or consensus) of multi‐agent systems, the method in this paper provides a more general framework by considering nonlinear multi‐agent systems with time delays and impulsive disturbances. The model in this paper is sufficiently general to include a class of delayed chaotic systems. Based on the Lyapunov stability theory and algebraic graph theory, sufficient conditions are presented to guarantee the cooperative exponential synchronization for these multi‐agent delayed nonlinear systems. These conditions are expressed in terms of linear matrix inequalities, which can easily be checked by existing software tools. It is seen that the Lyapunov functions must be constructed based on the graph topology to prove synchronization. The well‐known master–slave (drive‐response) synchronization of two chaotic delayed systems is a special case of this paper, and therefore, the results in this paper are also useful for practical applications in secure communication. Simulation results verify the effectiveness of the proposed synchronization control algorithm. Copyright © 2015 John Wiley & Sons, Ltd.     

对抗网络下时滞非线性多智能体系统固定时间二分一致性

本文针对一类存在输入时延的非线性多智能体系统,研究了其在结构平衡的无向符号图下的固定时间二分一致性问题.首先,本文针对智能体间相互合作与相互竞争的关系,设计了一类存在输入时延的多智能体系统固定时间分布式一致性控制协议,使得系统状态在固定时间内收敛到数值相同但符号相反的两个值,且收敛时间上界与初始状态无关.随后,利用Lyapunov稳定性理论和代数图论给出了在存在输入时延的情况下多智能体系统实现固定时间二分一致性的充分条件和收敛时间的上界值,证明了控制算法的稳定性.最后,仿真实例验证了所提固定时间二分一致性算法和理论结果的有效性.