Consensus problem of networked multi-agent systems with constant communication delay: stochastic switching topology case

This article proposes an observer-based control strategy for networked multi-agent systems with constant communication delay and stochastic switching topology. First, using the system transformation method, the mean-square consensus problem of multi-agent systems can be converted into the mean-square stability problem of an equivalent system, and some equivalent conditions concerning the mean-square consensus are presented. Then, an example is given to illustrate that the connection weights should be regarded as the parameters to be designed, since they have a great effect on the mean-square consensus of multi-agent systems. By choosing appropriate connection weights, the mean-square consensus problem can be converted into the mean-square stabilisation problem of N-1 delay systems with stochastic switching signal, whose related observer-based stabilisability criteria can be established in the form of linear matrix inequalities (LMIs). Furthermore, if the LMIs are feasible, the multi-agent systems achieve mean-square consensus if and only if the union of graphs in the switching topology set has a directed spanning tree. Finally, numerical simulations are given to illustrate our results.     

Second-order consensus of multi-agent systems with noises via intermittent control

Second-order consensus of multi-agent systems with noises via intermittent control is investigated in this paper. First, we study the mean-square consensus problem with communication noises by intermittent control. In order to reach consensus, under the strong directed interacted topology, by using the tools of graph theory and Lyapunov method, a distributed control protocol is proposed based on the noises and periodical intermittent information. The upper bound of noise strength in the sense of matrix norm and the lower bound of communication time duration are obtained. Second, a class of coupled system models which include delay-terms in their nonlinearities in the noisy environment is discussed. Under the balanced strongly connected topology, the sufficient conditions to achieve the mean-square average-consensus are obtained. Finally, simulations are given to illustrate the effectiveness of our results.     

Stochastic bounded consensus tracking of second-order multi-agent systems with measurement noises based on sampled-data with general sampling delay

This paper investigates the stochastic bounded consensus tracking problems of second-order multi-agent systems, where the control input of an agent can only use the information measured at the sampling instants from its neighbours or the virtual leader with a time-varying reference state, the measurements are corrupted by random noises and the signal sampling process induces the general sampling delay. First, the stochastic bounded consensus tracking protocol based on sampled-data with the general sampling delay is presented by using the delay decomposition technique. Second, the augmented matrix method, the probability limit theory and some other techniques are employed to derive the necessary and sufficient conditions guaranteeing the mean square bounded consensus tracking. The theoretical results show that the convergence of the proposed protocol simultaneously depends on the constant feedback gains, the network topology, the sampled period and the sampling delay, and that the static consensus tracking error depends on not only the above-mentioned factors, but also the noise intensity and the upper bound of the velocity and the acceleration of the virtual leader. The obtained results cover no sampling delay and the small sampling delay as two special cases. Simulations are provided to demonstrate the effectiveness of the theoretical results.     

受外界干扰的离散多智能体系统的均方有界一致性

对有外界干扰的二阶离散多智能体系统,研究了在马尔可夫切换拓扑结构下的均方有界一致性问题.首先,设计了一个带有智能体位置和速度信息的控制协议.其次,在随机有界干扰的情况下,借助于矩阵分析方法以及Lyapunov函数,得到了闭环系统实现均方有界一致所需的代数条件,同时给出了各智能体状态误差的上界.最后,数值仿真验证了理论结果的有效性.     

A Novel Leader-following Consensus of Multi-agent Systems with Smart Leader

This article studies the leader-following consensus problem for mixed-order multi-agent systems with a leader. Different from the traditional leader which is independent of all the other agents, the leader, called smart leader, can obtain and utilize the feedback information from its neighbors at some disconnected time intervals. A new distributed consensus control protocol based on intermittent control is developed for leader-following consensus with a smart leader. Moreover, the smart leader can adjust the control protocol based on the feedback information from its neighbors. With the aid of Lyapunov function, some sufficient conditions are derived for leader-following consensus of multi-agent systems with mixed-order dynamics under fixed directed topology. In addition, the similar results are obtained under switching directed topology. Finally, simulation results are provided to verify the correctness and effectiveness of theoretical results.     

具有随机丢包的网络化多自主体系统的一致性

研究具有随机丢包的网络化多自主体系统的均方一致性问题,其中不同自主体间的通信通道具有相同的丢包情况并且均服从马尔可夫(Markov)分布。首先,利用系统变换和迭代方法,得到了系统达到均方一致的一个初等充要条件。然后,利用矩阵理论和图论知识,如果拓扑图含有有向生成树,则可以将系统的均方一致性转化成一个线性Markov跳变系统的均方稳定性,并且可以建立线性矩阵不等式形式的均方可镇定准则。最后,通过相应的仿真实例说明了所得结论的可行性。     

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.     

Stochastic bounded consensus tracking of second-order multi-agent systems with measurement noises based on sampled-data with small sampling delay

This paper is devoted to the stochastic bounded consensus tracking problems of second-order multi-agent systems, where the control input of each agent can only use the information measured at the sampling instants from its neighbors or the virtual leader with a time-varying reference state, the measurements are corrupted by random noises, and the signal sampling process induces the small sampling delay. The augmented matrix method, the probability limit theory and some other techniques are employed to derive the necessary and sufficient conditions guaranteeing the mean square bounded consensus tracking. We show that the convergence of the proposed protocol simultaneously depends on the constant feedback gains, the network topology, the sampled period and the sampling delay, and that the static consensus tracking error depends on not only the above mentioned factors, but also the noise intensity and the upper bound of the velocity and the acceleration of the virtual leader. The obtained results cover no sampling delay as its one special case. Simulations are provided to demonstrate the effectiveness of the theoretical results.     

切换拓扑结构下多智能体系统的一致性研究

针对一类多智能体系统,研究了系统在切换拓扑结构下的一致性控制问题。假定系统拓扑结构的变化符合马尔可夫过程,设计与切换拓扑结构相关的一致性协议,利用线性矩阵不等式和随机稳定性理论,给出了多智能体系统满足一致性的充分条件,并通过数值仿真验证了所提控制方案的可行性和有效性。     

Leader-following consensus of nonlinear multi-agent systems with switching topologies and unreliable communications

In this paper, distributed leader-following consensus for a class of nonlinear multi-agent systems with switching topologies and unreliable communications is studied. Each possible topology contains a directed spanning tree rooted at the leader. Agents share the information only with their neighbors on some disconnected time intervals due to the unreliable communications. By designing suitable distributed controllers, all follower nodes asymptotically synchronize to the leader node if the communication rate is larger than a threshold value for each time interval. By using multiple Lyapunov functions theory and linear matrix inequalities technique, some sufficient conditions are given to guarantee the consensus. Moreover, based on the theoretical results, the admissible communication rate and convergence rate of the whole systems are adjusted by the feedback gain matrix, which provides helpful design guidelines in practical applications. Finally, a simulation example is given to verify the effectiveness of the proposed method.     

LQR‐based optimal topology of leader‐following consensus

In this paper, we consider the optimal topology for leader‐following consensus problem of continuous‐time and discrete‐time multi‐agent systems based on linear quadratic regulator theory. For the first‐order multi‐agent systems, we propose a quadratic cost function, which is independent of the interaction graph, and find that the optimal topology is a star topology. For the second‐order multi‐agent systems, a quadratic cost function is also constructed, whereas the optimal topology for second‐order leader‐following consensus problem is an unevenly weighted star topology. The universality of these findings means that if each follower is connected with the leader, the information exchange between followers is unnecessary and insufficient. Simulation examples are provided to illustrate the effectiveness of the theoretical results. Copyright © 2014 John Wiley & Sons, Ltd.     

Predictive Consensus for Networked Multi‐Agent Systems with Switching Topology and Variable Delay

This paper investigates consensus problems of networked linear time invariant (LTI) multi‐agent systems, subject to variable network delays and switching topology. A new protocol is proposed for such systems with matrix B that has full row rank, based on stochastic, indecomposable, aperiodic (SIA) matrix and the predictive control scheme. With the predictive scheme the network delay is compensated. Consensus analysis based on the seminorm is provided. The conditions are obtained for such systems with periodic switching topology to reach consensus. The proposed protocol can deal with time‐varying delays, switching topology, and an unstable mode. The numerical examples demonstrate the effectiveness of the theoretical results.     

Consensus control of multi-agent systems with missing data in actuators and Markovian communication failure

This article investigates the consensus problem of multi-agent systems (MASs) with imperfect communication both in channels and in actuators. The data transmission among agents may fail due to limited communication capacity, and the actuators may fail to receive information owing to noisy environment. We use a Markov chain approach to characterise the occurrence of the two types missing data in a unified framework. A sufficient consensus condition is first obtained in terms of linear matrix inequalities. Then, based on this condition, a novel controller design method is further developed such that the MAS with imperfect communication reaches mean-square consensus. It is shown that the consensus problem for MASs with switching topology can be regarded as a special case of the problem considered in this article, and the related theoretical results are presented as well. Numerical examples are provided to illustrate the effectiveness of the proposed approach.     

Passivity-based consensus for linear multi-agent systems under switching topologies

This paper studies the passivity-based consensus analysis and synthesis problems for a class of stochastic multi-agent systems with switching topologies. Based on Lyapunov methods, stochastic theory, and graph theory, new different storage Lyapunov functions are proposed to derive sufficient conditions on mean-square exponential consensus and stochastic passivity for multi-agent systems under two different switching cases, respectively. By designing passive time-varying consensus protocols, the solvability conditions for the passivity-based consensus protocol synthesis problem, i.e., passification, are derived based on linearization techniques. Numerical simulations are provided to illustrate the effectiveness of the proposed methods.     

Consensus based overlapping decentralized estimation with missing observations and communication faults

In this paper a new algorithm for discrete-time overlapping decentralized state estimation of large scale systems is proposed in the form of a multi-agent network based on a combination of local estimators of Kalman filtering type and a dynamic consensus strategy, assuming intermittent observations and communication faults. Under general conditions concerning the agent resources and the network topology, conditions are derived for the convergence to zero of the estimation error mean and for the mean-square estimation error boundedness. A centralized strategy based on minimization of the steady-state mean-square estimation error is proposed for selection of the consensus gains; these gains can also be adjusted by local adaptation schemes. It is also demonstrated that there exists a connection between the network complexity and efficiency of denoising, i.e., of suppression of the measurement noise influence. Several numerical examples serve to illustrate characteristic properties of the proposed algorithm and to demonstrate its applicability to real problems.     

Exponential Consensus for Nonlinear Multi‐Agent Systems with Communication and Input Delays via Hybrid Control

This paper aims to investigate the exponential leader‐following consensus for nonlinear multi‐agent systems with time‐varying communication and input delays by using hybrid control. Based on the Lyapunov functional method, impulsive differential equation theory and matrix analysis, we show that all the followers can achieve leader‐following consensus with the virtual leader exponentially even if only a fraction of followers can obtain the leader's information. Two classes of exponential consensus criteria as well as the convergence rates for the controlled multi‐agent systems are presented under very relaxed interaction topology conditions, i.e., the directed interaction topology among the followers is only required to have p(p>1) disjoint strong components. Finally, two numerical examples are given to validate the proposed theoretical results.     

Dynamic consensus of high-order multi-agent systems and its application in the motion control of multiple mobile robots

In this paper, the leader-following consensus problem for multi-agent linear dynamic systems is considered. All agents and leader have identical multi-input multi-output (MIMO) linear dynamics that can be of any order, and only the output information of each agent is delivered throughout the communication network. When the interaction topology is fixed, the leader-following consensus is attained by H∞ dynamic output feedback control, and the sufficient condition of robust controllers is equal to the solvability of linear matrix inequality (LMI). The whole analysis is based on spectral decomposition and an equivalent decoupled structure achieved, and the stability of the system is proved. Finally, we extended the theoretical results to the case that the interaction topology is switching. The simulation results for multiple mobile robots show the effectiveness of the devised methods.     

离散多智能体系统信息一致性的平衡点

研究了离散多智能体系统信息一致性的平衡点问题.对于固定通信结构系统,基于非负随机矩阵谱半径及其对应的左特征向量,证明了在系统的通信拓扑所含的生成树中,仅根节点对平衡点有作用.对于时变通信结构系统,根据同阶非负矩阵样式的有限性,证明了在动态通信拓扑的联合中,仅那些到任意节点都存在有向路径的顶点对平衡点有作用.数值算例验证了理论结果的正确性.     

Distributed leader-following consensus for second-order multi-agent systems with nonlinear inherent dynamics

In this paper, the leader-following consensus problem for second-order multi-agent systems with nonlinear inherent dynamics is investigated. Two distributed control protocols are proposed under fixed undirected communication topology and fixed directed communication topology. Some sufficient conditions are obtained for the states of followers converging to the state of virtual leader globally exponentially. Rigorous proofs are given by using graph theory, matrix theory and Lyapunov theory. Simulations are also given to verify the effectiveness of the theoretical results.     

Iterative Consensus for a Class of Second-order Multi-agent Systems

In this paper, the problem of leader-following consensus for a class of multi-agent systems with double integrator dynamics is investigated based on an iterative learning approach. Consensus errors of individual agents are considered as the anticipation in time, based on which a distributed iterative learning protocol is proposed for the undirected networks with fixed topology to make the followers track the leader in finite time. The dynamic of the leader is assumed to be time-varying and the state information is available to only a portion of the followers. The sufficient condition for solving the consensus problem of the multi-agent system is obtained. A simulation example is provided to demonstrate the effectiveness of the proposed method.