Research On The Consistency Problem Of Multi-agent System Under Random Switching Topolog

Multi-agent system is one of the important branches in the intelligent control field,which is widely used in aerospace,smart power grid,traffic management and other fields.Cooperative control is the main research subject of multi-agent system,and consensus problem is the basic problem of cooperative control.In this dissertation,the consensus problems of nonlinear multi-agent systems are studied in the sense of random switching topology,which has covered three cases: Fixed-time random switching,Markov switching and semi-Markov switching.The specific research contents are as follows:Firstly,the consensus problem of multi-agent system with noise interference is studied under the random topology with fixed-time switching.In the first place,the consensus protocol is constructed,then the original system is transformed into a stochastic differential system with It^o type by means of graph theory and Kronecker product.By using the theoretical knowledge comprehensively such as algebraic graph theory,stochastic differential equation,Lyapunov stability theory and so on,the mean-square consensus criterion based on expected augmented Laplacian matrix is established.Further on,by using matrix decomposition method,we propose the consensus criterion which is weakly dependent on the topology information in the switching topology composed of balanced digraphs.Secondly,under the Markov switching topology,the consensus problem of multiagent systems with mode-dependent delays is studied by stochastic sampling control protocol.By introducing two auxiliary delay functions and a Bernoulli random variable,the original system is firstly transformed into a Markov jump system with random timevarying delays.For the directed topology case,the mean-square consensus criterion which depends on the maximum mode-dependent delay and sampling periods is established by using stochastic analysis theory and matrix inequalities method.Meanwhile,the allowable intervals of the coupling intensity coefficient and the maximum mode-dependent delay are given.Furthermore,the dimension-reduced mean-square consensus criterion is derived for the undirected topology case.Finally,we extend the Markov switching topology case to the more general semiMarkov switching topology case.The consensus problems of multi-agent systems under the sampled-data-based event-triggered control is studied.The original system with measurable states is firstly transformed into a hybrid system with semi-Markov jump parameters.Then,by means of the approaches such as Schur’s complement lemma,convex combination technique and free relaxation matrix method and so on,the meansquare consensus criteria are derived respectively for two cases: The transition rates are fully and partially known.On this basis,the relevant methods and theories are extended to the unmeasurable system states case.By introducing the free weight matrix method,the theoretical criteria for the multi-agent system to achieve the exponentially mean-square consensus are established.