Study On Group Consensus Of Multi-agent Systems With Time Delay

Recently, coordination control problem of multi-agent systems has been extensively applied in engineering applications, such as no unmanned vehicle system of formation coordination, clock synchronization of sensor networks, the satellite attitude synchronization etc., so it has attracted intensive study from many fields including physics, computer science and automatic control subjects. As the most basic and most important problem in coordination control of multi-agent systems, consensus problem implies that all the agents’ states reach an identical common value by locally coupling coordination. The agents are required to make corresponding response to the varying environment, unknown conditions and diverse cooperative tasks, so the whole multi-agent system may be divided into several sub-groups converging to different final consensus state, which is named as group consensus problem.Inevitably, time delays exist in the process of information exchange between neighboring agents, so analyzing delay effect on the group consensus problem of multi-agent system has more practical significance. This paper mainly studies the group consensus of multi-agent systems with time-varying communication delay. The main contents include:1. Considering the time-varying communication delay effect on group consensus convergence, we adopt synchronous and asynchronous coupling algorithms, respectively, to deal with the group consensus problem for the multi-agent systems composed of second-order integrators. By using variable substitution for the multi-agent system, group consensus convergence problem is transformed into the stability of the reduced-order system. According to graph theory and Lyapunov-Krasovskii functional, we obtained sufficient conditions for second-order multi-agent systems subject to time-varying communication delay reaching an asymptotic group consensus.2. For a class of heterogeneous multi-agent system consisting of first-order and second-order integrators, we analyze the stationary group consensus problem with time-varying delays. In addition, two consensus protocols under fixed interconnection topology and switching topologies, respectively, are proposed for the heterogeneous multi-agent system converging to group consensus asymptotically. Based on Lyapunov-Krasovskii functional, sufficient conditions in the form of linear matrix inequalities are obtained for the agents achieving asymptotic group consensus under the group consensus algorithm with identical time-varying communication delay, and the free weight matrix is introduced in order to reduce the conservative conditions.3. Scaled group consensus convergence problem is analyzed for the multi-agent systems with agent’s dynamics modeled by second-order integrators, and the dynamical and stationary consensus protocols are designed respectively. In order to eliminate the strict assumptions on the negative coupling weights of the synergetic and competitive method, which is usually adopted to deal with the group consensus problem of multi-agent systems, we introduce proportional coefficient in the consensus protocol, which makes the states of agent in same sub-group reach an identical value asymptotically and the states of agent in different sub-groups reach assigned proportions. Firstly, stationary and dynamical group consensusproblems are analyzed for the second-order multi-agent systems with directed interconnection topology by matrix and graph theory. Then, scaled group consensus problems are investigated for the second-order multi-agent systems with time-varying communication delay driven by the dynamical and stationary consensus protocols, respectively, in synchronously-coupled forms, and delay-dependent sufficient consensus conditions in the form of linear matrix inequalities are obtained.