Consensus problem of heterogeneous multi-agent systems with time delay under fixed and switching topologies

Consensus problem is investigated for heterogeneous multi-agent systems composed of first-order agents and second-order agents in this paper. Leader-following consensus protocol is adopted to solve consensus problem of heterogeneous multi-agent systems with time-varying communication and input delays. By constructing Lyapunov-Krasovkii functional, sufficient consensus conditions in linear matrix inequality(LMI) form are obtained for the system under fixed interconnection topology. Moreover, consensus conditions are also obtained for the heterogeneous systems under switching topologies with time delays. Simulation examples are given to illustrate effectiveness of the results.     

Consensus of multi-agent linear dynamic systems via impulsive control protocols

In this article, we introduce impulsive control protocols for multi-agent linear dynamic systems. First, an impulsive control protocol is designed for network with fixed topology based on the local information of agents. Then sufficient conditions are given to guarantee the consensus of the multi-agent linear dynamic systems by the theory of impulsive systems. Furthermore, how to select the discrete instants and impulsive matrices is discussed. The case that the topologies of networks are switching is also considered. Numerical simulations show the effectiveness of our theoretical results.     

An LMI Approach to consensus in second-order multi-agent systems

This paper deals with the consensus problem of the second-order multi-agent systems based on linear system theory. By a system transformation, the consensus problem is converted to the stability problem of a linear system. The second-order systems considered include the systems with both the fixed topology and the Markov switching topology. Necessary and sufficient conditions of consensus or mean square consensus are obtained. The results are extended to the cases of the uncertain transition probability rates and time-delay, respectively. Finally, a simulation example is given to show the effectiveness of the presented results.     

异构多智能体系统有限时间一致性分析

研究二阶智能体速度不可测情况下由一阶和二阶智能体构成的异构多智能体系统有限时间一致性问题。在固定拓扑结构下,给出了异构系统实现一致性的控制协议,通过LaSalle不变集原理和齐次控制方法得到了异构系统有限时间一致性的充分条件;在切换拓扑结构下,给出了异构系统一致性的控制协议,得到了异构系统有限时间一致性的充分条件。仿真结果验证了相关结果的有效性。     

异质多智能体系统二分一致性的充要条件

针对由一阶智能体和二阶智能体组成的异质多智能体系统的二分一致性问题,对连续和离散系统情形分别设计了二分一致性协议。基于结构平衡的拓扑,通过规范变换实现了从具有敌对关系的系统到具有非负连接权重系统的转化,将二分一致性问题转变为一般一致性问题。进一步,运用代数图论和矩阵理论分析闭环控制系统的动态特性,得到了异质多智能体系统渐近实现二分一致性的充要条件。最后通过数值模拟验证了所得结果的有效性。     

二阶多智能体系统采样控制的一致性

研究在固定拓扑和切换拓扑下,二阶多智能体系统通过采样控制的一致性问题。首先,对于固定拓扑,给出了二阶多智能体系统通过采样控制达到一致性的充要条件;其次,对于切换拓扑,在所有联合切换拓扑有生成树的前提下,建立基于控制参数和采样周期使二阶系统实现一致性的充分条件。最后,用数值仿真验证所给结论的有效性。     

Group consensus control for heterogeneous multi-agent systems with fixed and switching topologies

In this paper, the group consensus problems of heterogeneous multi-agent systems with fixed and switching topologies are investigated. First, a class of distributed group consensus protocol is proposed for achieving the group consensus of heterogeneous multi-agent systems by using the neighbours’ information. Then, some corresponding sufficient conditions are obtained to guarantee the achievement of group consensus. Rigorous proofs are given by using graph theory, matrix theory and Lyapunov theory. Finally, numerical simulations are also given to verify the theoretical analysis.     

一类异质多智能体系统的一致性控制

针对一类由连续时间一阶和二阶智能体组成的异质多智能体系统,首先给出一阶和二阶智能体实现一致性的算法,其次利用图论和矩阵理论相关知识,在固定有向拓扑结构下,给出异质多智能体系统实现一致性的充要条件,且在一致性实现时给出一致性状态的确切表达式;在切换拓扑结构下,给出异质多智能体系统实现一致性的充分条件。最后给出数值算例验证了相关结论的有效性。     

Distributed consensus for multi-agent systems with delays and noises in transmission channels

This paper studies the distributed consensus problem for linear discrete-time multi-agent systems with delays and noises in transmission channels. Due to the presence of noises and delays, existing techniques such as the lifting technique and the stochastic Lyapunov theory are no longer applicable to the analysis of consensus. In this paper, a novel technique is introduced to overcome the difficulties induced by the delays and noises. A consensus protocol with decaying gains satisfying persistence condition is adopted. Necessary and sufficient conditions for strong consensus and mean square consensus are respectively given for non-leader–follower and leader–follower cases under a fixed topology. Under dynamically switching topologies and randomly switching topologies, sufficient conditions for strong consensus and mean square consensus are also obtained. Numerical examples are given to demonstrate the effectiveness of the proposed protocols.     

时延异构多自主体系统的群一致性分析

针对由一阶自主体和二阶自主体构成的异构多自主体系统的静态群一致性问题,分别提出了在固定连接拓扑和切换连接拓扑结构下的静态群一致性算法。通过构造Lyapunov-Krasovskii函数,得到了系统在具有相同时变通信时延的群一致性算法作用下渐近收敛群一致的充分条件,并以线性矩阵不等式表示。最后,仿真结果表明,所提算法在满足一定条件下能使时延异构多自主体系统渐近收敛群一致。     

Stochastic consensus seeking with communication delays

This paper investigates the consensus problem of dynamical networks of multi-agents where each agent can only obtain noisy and delayed measurements of the states of its neighbors due to environmental uncertainties and communication delays. We consider general networks with fixed topology and with switching (dynamically changing) topology, propose consensus protocols that take into account both the noisy measurements and the communication time-delays, and study mean square average-consensus for multi-agent systems networked in an uncertain environment and with uniform communication time-varying delays. Using tools from differential equations and stochastic calculus, together with results from matrix theory and algebraic graph theory, we establish sufficient conditions under which the proposed consensus protocols lead to mean square average-consensus. Simulations are also provided to demonstrate the theoretical results.     

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.     

异质多智能体系统滞后一致性跟踪控制

针对一阶、二阶混合异质多智能体系统的滞后一致性问题,提出了一种基于牵制控制的分布式滞后一致性控制协议。首先,将滞后一致性分析转化为稳定性证明;然后,利用图论和Lyapunov稳定性理论分析闭环系统稳定性;最后,分别在固定拓扑和切换拓扑结构下给出了基于线性矩阵不等式（LMI）形式的滞后一致性可解的充分条件,从而实现异质多智能体的领导-跟随者滞后一致性。数值仿真结果表明,所提出的滞后一致性控制方法可以使异质多智能体系统实现领导-跟随者滞后一致性。     

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.     

Allowable delay bound for consensus of linear multi-agent systems with communication delay

This paper studies the consensus of a group of linear dynamic agents with a uniform communication delay and focuses on searching an allowable delay bound. As long as the delay is less than this bound, there exist linear feedback consensus protocols driving the multi-agent system to achieve consensus. Both fixed and switching topology cases are investigated. In both cases, the consensus problem is converted to the robust stability problem of corresponding uncertain state-delayed systems. By using Lyapunov–Krasovskii functional analysis, consensus conditions which contain the feedback gain conditions and delay conditions are proposed for systems over fixed and switching topologies, respectively. Furthermore, allowable delay bounds are obtained for both systems by solving the optimal robust stabilisation problems. Numerical examples are given to illustrate the results.     

具有动态领导节点的多智能体系统一致性分析

具有领导节点的一致性问题是多智能体协调控制重要研究内容。目前其研究结论主要集中在系统通信拓扑关系固定不变这一前提下,对于系统通信拓扑关系为动态变化时具有领导节点的一致性问题尚未得到完全解决。对系统通信拓扑关系为有向、时变情况下的具有领导节点的多智能体系统一致性问题进行研究。分析并给出了在领导节点为常值和时变两种情况下多智能体系统达到一致的条件。并通过矩阵论和图论相关知识给出了详细证明。最后通过仿真实例验证了结论的正确性。     

线性和非线性动态异构多自主体系统的有限时间一致性（英文）

In this paper, the finite-time consensus problems of heterogeneous multi-agent systems composed of both linear and nonlinear dynamics agents are investigated. Nonlinear consensus protocols are proposed for the heterogeneous multi-agent systems.Some sufficient conditions for the finite-time consensus are established in the leaderless and leader-following cases. The results are also extended to the case where the communication topology is directed and satisfies a detailed balance condition on coupling weights.At last, some simulation results are given to illustrate the effectiveness of the obtained theoretical results.     

线性和非线性动态异构多自主体系统的有限时间一致性

研究了由线性和非线性动态自主体组成的异构多自主体系统的有限时间一致性问题.针对该异构系统提出了非线性的一致性协议,并分别给出了无领航者和有领航者情形下异构系统在有限时间内实现一致性的充分条件.所得结果还推广到具有有向通信拓扑且满足细致平衡条件的多自主体系统情形.最后,给出一些仿真结果来验证所得结论的正确性和有效性.     

具有时滞的混合阶多智能体系统的组一致性

针对由离散时间一阶和二阶智能体组成的混合阶多智能体系统,研究其在固定和切换拓扑结构下受通信时滞影响时的组一致性问题。分别为两类智能体提出组一致性协议,引入模型变换,将闭环系统转化为等价系统。在一定假设条件下,以代数图论、矩阵理论为主要研究工具,分别在固定和切换拓扑结构下给出了混合阶多智能体系统实现渐近组一致性的条件。采用数值仿真对所得结果的有效性进行了验证。     

Controllability of heterogeneous multi-agent systems under directed and weighted topology

This paper considers the controllability problem for both continuous- and discrete-time linear heterogeneous multi-agent systems with directed and weighted communication topology. First, two kinds of neighbour-based control protocols based on the distributed protocol of first-order and second-order multi-agent systems are proposed, under which it is shown that a heterogeneous multi-agent system is controllable if the underlying communication topology is controllable. Then, under special leader selection, the result shows that the controllability of a heterogeneous multi-agent system is solely decided by its communication topology graph. Furthermore, some necessary and/or sufficient conditions are derived for controllability of communication topology from algebraic and graphical perspectives. Finally, simulation examples are presented to demonstrate the effectiveness of the theoretical results.