Stability Analysis Of Agent Systems And Its Applications In Consensus Of Multi-agent Systems

With the rapid development of wireless communication and networked technology,the researches on problems of multi-agent systems have been greatly developed.The multi-agent systems can effectively accomplish some relatively complex production and life tasks through coordination among agents.Therefore,multi-agent systems provide many applications in various practical fields,such as military,industrial production,aerospace etc.As the basis of coordinated control,stability and consensus control are the most important research areas in multi-agent systems.To achieve stability and consensus of multi-agent systems,the first step is to ensure stability of each individual agent in the systems.In this paper,based on the analysis of the shortcomings of the existing research on stability and consensus of agent systems,the problems of stability of a single agent system,multi-target selection,formation and consensus tracking in multi-agent systems are discussed in detail.The main research works are summarized as follows:(1)For the problem of stability of a single-agent system in Banach spaces,a new method using fixed point iterative algorithm is proposed to solve the problem.First,a new fixed point iterative algorithm in Banach spaces is presented,and the strong convergence of the algorithm is proved by using the fixed point theory.Then,the proposed iterative algorithm is applied to the stability problems of a single agent system,where each point in the iterative sequence is regarded as the moving locus of the single agent system,and the sequence converges to a specific point,means that the single agent system is in a stable state.(2)For the problem of stability of a single-agent system in Hilbert spaces,and the complexity of the implicit iterative algorithm given in Banach spaces,a simpler and intuitionistic explicit fixed point iteration algorithm in Hilbert spaces is given.Then the new iterative algorithm is applied to solve the problem of stability for a single agent system.(3)For the problem of stability of a single-agent system in networked environment,the stability of a single agent system with time delay and quantization is studied.In theresearch,delay decomposition and logarithmic quantizer are introduced to make full use of time delay and quantization information.At the same time,the stability condition of the single-agent system is given by selecting the enhanced Lyapunov function,and the results are given in the form of linear matrix inequality,which can be easily optimized.(4)For the targets selection and consensus formation problems in multi-agent systems,an improved dynamic method based on auction algorithm is proposed,and the formation control strategy with offset is proposed for the agents which selecting the same target.Two situations are discussed: system with a leader and without a leader.Furthermore,the event-triggered control mode instead of time-triggered control mode is added to targets selection and formation,which can save bandwidth resources and energy while ensuring stability of the system.(5)For the problems of consensus tracking problems of leader-following multi-agent systems,the communication time-varying delay and actuator saturation are considered.First,by setting a saturation bound,the input of the system is limited to a fixed interval.Then the distributed consensus tracking controllers of the leader agent and the following agents are designed separately.The effect of time-varying delay is considered in the design of the controller,and the Lyapunov function is constructed,which gives conditions of stability for the system and proves that the system is closed-loop stable under the given controllers.