Consensus strategy for a class of multi‐agents with discrete second‐order dynamics

This paper investigates consensus strategies for a group of agents with discrete second‐order dynamics under directed communication topology. Consensus analysis for both the fixed topology and time‐varying topology cases is systematically performed by employing a novel graph theoretic methodology as well as the classical nonnegative matrix theory. Furthermore, it is shown that the necessary and sufficient condition for the agents under fixed communication topology to reach consensus is that the communication topology has a spanning tree; and sufficient conditions for the agents to reach consensus when allowing for the dynamically changing communication topologies are also given. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed results. Copyright © 2011 John Wiley & Sons, Ltd.     

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。     

Consensus seeking of high-order dynamic multi-agent systems with fixed and switching topologies

This article studies a consensus problem for a group of high-order dynamic agents with fixed and switching topologies. Two linear consensus protocols, which only depend on the agent's own information and its neighbours' partial information, are proposed, respectively, for the group with and without communication time-delays. For the case of fixed topology and zero communication time-delay, a necessary and sufficient condition for the consensus is established. The parameter design of the protocol is also discussed. Under switching topology, the consensus is investigated for two cases: the case of zero communication time-delay and the case of nonuniform communication time-delays. For each case, a sufficient condition for the consensus is provided. Moreover, for a group of double/triple-integrator agents with fixed topology and uniform constant time-delay, some necessary and sufficient conditions for the consensus are given. Finally, numerical simulations are worked out to illustrate the effectiveness of the theoretical results.     

Consensus for multi‐agent systems under double integrator dynamics with time‐varying communication delays

In this paper, the consensus control problems for multi‐agent systems under double integrator dynamics with time‐varying communication delays are investigated. We assume that the interaction graphs among agents are directed. Two kinds of protocols are considered. One is an absolute damping protocol, and the other is a relative damping protocol. For the first protocol, Lyapunov–Razumikhin functional techniques are used. We derive sufficient conditions that guarantee that all agents asymptotically reach consensus under fixed topology and switching topology, respectively. Moreover, the allowable upper bound for communication delays is given. For the second protocol, Lyapunov–Krasovskii functional techniques are used. Linear matrix inequality (LMI)‐form sufficient conditions are obtained to guarantee the consensus problems to be solved under fixed topology and switching topology, respectively. The allowable upper bound for communication delays is given as well. The feasibilities of the demanded LMIs are also discussed. Finally, numerical simulations are provided to illustrate the effectiveness of our theoretical results. Copyright © 2011 John Wiley & Sons, Ltd.     

多图通信拓扑下一致性系统的鲁棒性度量

研究在外界扰动影响下的通信拓扑为多图的一阶多智能体系统的协同一致性控制鲁棒性问题. 采用闭环系统的??₂ 范数来度量系统的鲁棒性; 借助代数图论、控制论和矩阵论, 建立通信拓扑在有无自环时多智能体系统鲁棒性、系统??₂ 范数、系统通信拓扑之间的直接联系, 并进行严格的证明; 给出通信拓扑为完备图、星图、路图、环图时多智能体系统之间的收敛速度、鲁棒性分析与比较. 仿真实例表明了所提出方法的有效性.

     

多智能体沿多条给定路径编队运动的有向协同控制

研究了在有向通信连接下二阶积分器描述的多智能体沿多条给定路径编队运动的控制器设计及其稳定性分析问题. 智能体的动态和指定路径都是在固定直角坐标系下描述的. 通过引入路径函数来设计路径跟踪控制, 根据路径函数与弧长的关系来设计编队控制律, 使得多智能体沿期望路径的位置和速度在规定队形下达到一致. 利用图论证明, 当通信拓扑对应的有向图具有全局可达点时, 设计的编队控制系统是渐近稳定的. 本文设计的有向协同控制律可以应用于区域的信息优化采集.     

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.     

Consensus in multi‐agent systems with communication constraints

The problem of second‐order consensus is investigated in this paper for a class of multi‐agent systems with a fixed directed topology and communication constraints where each agent is assumed to share information only with its neighbors on some disconnected time intervals. A novel consensus protocol designed based on synchronous intermittent local information feedback is proposed to coordinate the states of agents to converge to second‐order consensus under a fixed strongly connected topology, which is then extended to the case where the communication topology contains a directed spanning tree. By using tools from algebraic graph theory and Lyapunov control approach, it is proved that second‐order consensus can be reached if the general algebraic connectivity of the communication topology is larger than a threshold value and the mobile agents communicate with their neighbors frequently enough as the network evolves. Finally, a numerical example is simulated to verify the theoretical analysis. Copyright © 2011 John Wiley & Sons, Ltd.     

Periodic intermittent consensus of second-order agents networks with nonlinear dynamics

The consensus problem for a class of second-order agents networks via periodically intermittent control is investigated in this paper. A novel protocol is designed by periodic intermittent measurements and directed topology. Based on algebraic graph theory, matrix theory and Lyapunov control approach, some sententious conditions are obtained for reaching consensus in agents networks with fixed topology. Finally, one example is given to illustrate the effectiveness of the theoretical results.     

积分事件触发策略下的线性多智能体系统领导跟随一致性

研究有向切换拓扑下线性多智能体系统的事件触发一致跟踪问题.大多数已有的工作研究了固定拓扑下的事件触发控制,然而,当智能体间联系随时间发生改变或通信拓扑随时间发生变化时,该控制策略失效.鉴于此,在考虑切换拓扑的基础上提出一种基于积分型事件触发的控制策略.首先,当拓扑图包含一棵生成树且领导者是根节点时,利用Lyapunov稳定性理论、代数图论和矩阵变换,基于积分型事件触发控制协议,在切换拓扑下多智能体系统达到领导跟随一致性;然后,当存在多个领导者时,基于设计的触发机制在切换拓扑下多智能体系统实现包含控制,上述两种情况下闭环系统均不存在Zeno现象;最后,通过仿真结果验证控制策略的有效性.     

Consensus problems in networks of agents with switching topology and time-delays

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 disagreement function that is a common Lyapunov function for the disagreement dynamics of a directed network with switching topology. A distinctive feature of this work is to address consensus problems for networks with directed information flow. We provide analytical tools that rely on algebraic graph theory, matrix theory, and control theory. Simulations are provided that demonstrate the effectiveness of our theoretical results.     

基于有向网络的智能群体群集运动控制

对具有二次积分动态的智能群体(flock/swarm),在有向网络取得群集运动(flocking/swarming)进行了研究．提出了一个分散控制方法对智能群体进行分散控制．用有向图模型表示智能体之间的相互作用及通信关系．对固定的网络拓扑,控制互连拓扑是固定的,时不变的,运用传统的LaSalle不变集原理,代数图论的有关技巧进行了稳定性分析,并得到以下主要结论:i)智能群体速度方向渐进收敛,并保持方向一致;ii)智能群体速度大小渐进收敛,并保持大小相等;iii)有邻接关系的智能体(Agent)之间没有碰撞发生;iv)智能群体的势场函数被最小化．理论分析显示,有向图的弱连通性及一种称为平衡图的有向图在系统的稳定性分析中扮演着关键角色．最后,给出了一个仿真例子对理论结果进行了验证．     

多星系统相对轨道的自适应协同控制

基于一致性理论,在无向拓扑结构上对多星系统相对轨道的协同控制问题进行了研究.本文考虑近地卫星相对轨道的非线性方程,首先设计控制律使得多星系统形成目标队形,并给出了速度阻尼和通信拓扑(相对速度间的拓扑关系)连通性之间的关系;其次,针对卫星质量具有不确定性的情形,设计了新的辅助变量,提出了自适应的协同控制律,这里要求传感(相对位置间的拓扑关系)和通信具有相同的拓扑结构.最后对4颗卫星的编队飞行进行了仿真分析,仿真结果表明本文设计的协同控制律是有效可行的.     

Average consensus in networks of dynamic agents with switching topologies and multiple time-varying delays

In this paper, we discuss average consensus problem in undirected networks of dynamic agents with fixed and switching topologies as well as multiple time-varying communication delays. By employing a linear matrix inequality method, we prove that all the nodes in the network achieve average consensus asymptotically for appropriate communication delays if the network topology is connected. Particularly, several feasible linear matrix inequalities are established to determine the maximal allowable upper bound of time-varying communication delays. Numerical examples are given to demonstrate the effectiveness and the sharpness of the theoretical results.     

Consensus control of output‐constrained multiagent systems with unknown control directions under a directed graph

This paper presents a novel distributed adaptive control algorithm for uncertain higher‐order nonlinear multiagent systems subject to output constraints and unknown control directions. Regarding the latter, a generic class of cases is considered, allowing completely unknown and even nonidentical control directions. Furthermore, the communication topology is only required to contain a fixed directed spanning tree. To guarantee the output constraints and address the asymmetric directed communication topology, a new reference output using the transformation strategy is introduced for each agent, benefiting from which the consensus problem of the multiagent system is recast as local tracking control problems of single agents. Then, the distributed control algorithm is recursively established based on the backstepping technique and the Nussbaum‐type function. By leveraging the unique properties of the Laplacian matrix on directed graphs and matrix theory, it is shown that, under the proposed distributed algorithm, uniform boundedness of all closed‐loop signals can be ensured, and asymptotic consensus is achieved without violation of the output constraints. Finally, simulation studies on the angle control of single‐link robots are given to verify the effectiveness of the proposed algorithm.     

具有通信时延的二阶多智能体系统有限时间一致性跟踪控制

针对具有通信时延的二阶多智能体系统的有限时间一致性控制问题,分别研究了具有固定拓扑和切换拓扑网络结构情形下的二阶多智能体系统的有限时间一致性。为使多智能体系统能在有限时间内可以达到一致,引入一致性控制增益矩阵并设计了相应的基于相对位置和相对速度的时延状态误差有限时间一致性控制算法,利用系统模型转换,泛函微分方程稳定性理论和有限时间Lyapunov稳定性定理得到了使系统在有限时间内达到一致跟踪的最大时延上界值。最后,仿真实验结果验证了所得理论的正确性和有效性。     

Consensus for linear multi-agent system with intermittent information transmissions using the time-scale theory

This paper investigates the consensus problem for linear multi-agent system with fixed communication topology in the presence of intermittent communication using the time-scale theory. Since each agent can only obtain relative local information intermittently, the proposed consensus algorithm is based on a discontinuous local interaction rule. The interaction among agents happens at a disjoint set of continuous-time intervals. The closed-loop multi-agent system can be represented using mixed linear continuous-time and linear discrete-time models due to intermittent information transmissions. The time-scale theory provides a powerful tool to combine continuous-time and discrete-time cases and study the consensus protocol under a unified framework. Using this theory, some conditions are derived to achieve exponential consensus under intermittent information transmissions. Simulations are performed to validate the theoretical results.     

非线性随机多智能体系统的固定时间一致性

本文研究了在固定拓扑和切换拓扑下,非线性随机多智能体系统的固定时间一致性问题.首先针对固定拓扑,设计了一种非线性控制协议,利用随机Lyapunov稳定性理论和代数图论给出了实现固定时间一致性的充分条件和收敛时间的上界值,随后将结论推广至切换拓扑,设计的切换拓扑子图的并集只需要满足连通条件,即可实现固定时间一致,模型更具...     

Asynchronous Consensus in Continuous-Time Multi-Agent Systems With Switching Topology and Time-Varying Delays

The paper studies asynchronous consensus problems of continuous-time multi-agent systems with discontinuous information transmission. The proposed consensus control strategy is implemented based on the state information of each agent's neighbors at some discrete times. The asynchrony means that each agent's update times, at which the agent adjusts its dynamics, are independent of others'. Furthermore, it is assumed that the communication topology among agents is time-dependent and the information transmission is with bounded time-varying delays. If the union of the communication topology across any time interval with some given length contains a spanning tree, the consensus problem is shown to be solvable. The analysis tool developed in this paper is based on nonnegative matrix theory and graph theory. The main contribution of this paper is to provide a valid distributed consensus algorithm that overcomes the difficulties caused by unreliable communication channels, such as intermittent information transmission, switching communication topology, and time-varying communication delays, and therefore has its obvious practical applications. Simulation examples are provided to demonstrate the effectiveness of the theoretical results.     

Fuzzy adaptive iterative learning coordination control of second-order multi-agent systems with imprecise communication topology structure

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.