Consensus Of Multi-agent Systems Based On Adaptive Control And Communication Constraints

The coordination control of multi-agent systems is a hot topic in the artificial intelligence and system control.In the control,each agent needs to achieve a common goal or more than one aspects through interaction and show a consistent state.Therefore,the consensus of multi-agent systems is one of the important problems of coordination control,and has received significant research from various scientific.The main task is to design an appropriate protocol based only on the local relative information.In this paper,several different control strategies including edged-based adaptive control,directed spanning tree based adaptive control,aperiodic intermittent control,intermittent sampled-data control and guaranteed cost control are proposed to investigate the consensus of multi-agent systems.In the first part,the consensus problem of second-order multi-agent systems via adaptive protocol is studied.First,based only on local information of the network structure,the edge-based adaptive protocol which assigns a time-varying coupling weight to each edge in the communication is proposed.The consensus problems of the network with and without leader via the protocol are considered.The coupling gains can be chosen randomly in the protocol and the consensus can be reached without satisfying any additional conditions.Moreover,the consensus problem of second-order multi-agent systems with directed topology is discussed.A directed spanning tree based adaptive control protocol is designed.Applying the developed method and Lyapunov stability theory,some distributed adaptive laws are designed in the directed network.It is found that the consensus can be achieved by randomly choosing a directed spanning tree and using the developed distributed adaptive laws.In the second part,on the one hand,the consensus problem for second-order multiagent systems via aperiodically intermittent control is investigated.Two types of time delays are considered.The first case is that the delay is small enough so that it is less than the minimum of communication width.The other one is that the delay is timevarying and large.In this case,we don't restrict the delay less than communication width.Different approaches are provided to study these two cases,and based on the matrix theory and the Lyapunov stability theory,some conditions are obtained to achieve second-order consensus.On the other hand,the periodic intermittent sampled data control strategies with and without the time delay are proposed to investigate the second-order consensus of multi-agent systems.In order to reach consensus,some necessary and sufficient conditions depending on the coupling gains,the communication width,the sampling period and the spectrum of the Laplacian matrix,are established.For the case with time delay.It is amazing found that the sampling period should has both lower and upper bounds for the sake of reaching consensus.In the third part,the leaderless consensus problem of multi-agent systems with nonlinear dynamics and directed switching communication graphs is considered.The assumption in previous work that each possible communication graph contains a directed spanning tree is relaxed in this part.Based on the directed spanning tree,an error system which well transforms the consensus problem into the stabilization problem is proposed.By using matrix analysis theory and stability analysis of the nonlinear systems,a new kind of multiple Lyapunov function which depends on the communication graphs,is designed for analyzing the consensus behavior.It is theoretically shown that the consensus can be achieved if the coupling gain is carefully chosen and other threshold conditions based on the communication graphs are satisfied.Finally,the guaranteed cost consensus problem for second-order multi-agent systems with heterogeneous inertias is considered.In the existing guaranteed cost consensus protocols,all agents are assumed to have a common inertias or share control gains,and the communication topology is always undirected.However,in this part,we suppose that the inertias and the control gains are heterogeneous,and the communication topology is directed.The distributed protocols with absolute and relative velocity dampings are proposed,respectively,in which both the communication with and without the time delays are also considered.By introducing the auxiliary variables and using Lyapunov stability theory,some sufficient conditions are given to achieve the consensus for all these protocols and the upper bound of the performance functions are obtained.