Research On The Distributed Consensus Control For Multi-Agent Systems With Stochastic Noises

This thesis is devoted to the study of consensus control of multi-agent systems with stochastic noises.Three cases of multi-agent systems are considered.They are the multi-agent systems with additive system noises,with multiplicative system noises,and with both constraint and additive noises,respectively.The critical methods to deal with these consensus problems include Lyapunov theory,projection,matrix analysis,parameterized Riccati inequalities,and so on.Algebra Riccati equation and Lyapunov equation are the basic technical tools to solve the stability problem of a linear system.In this thesis,the consensus protocols are proposed based on the algebra Riccati equation and the structure of the communication topology.Under this protocol,the consensus error of the multi-agent systems with additive noises are characterized,and the consensus error of the leader-follower multi-agent systems with additive noises are characterized by the same means.Furthermore,for the case of the multi-agent systems with multiplicative noises,sufficient conditions for mean-square consensusability are obtained based on the parameterized Riccati inequalities and communication topology.Finally,for the multi-agent systems with bounded constraint and additive noises,the sufficient conditions for mean-square asymptotically constrained consensus are obtained based on the method of weighted average and projection.The contribution and the novelty of this work lies in that:For the case of multi-agent systems with additive system noises,the consensus error is characterized based on the solutions to the algebra Riccati equation and Lyapunov equation,the proposed approach are superior to the existing result that applying Kalman filtering theory to computing the consensus error;For the case of multi-agent systems with multiplicative noise,sufficient conditions are given under which the mean-square consensus can be realized;For the case of the multiagent systems with both additive noises and bounded constraint,the mean-square constraint consensus problem is solved.The results of this work include the following aspects.(1)The problem of characterization of the consensus error for the multiagent systems with additive system noises is studied.As is known to all,the exact consensus cannot realized for the multi-agent systems with additive system noises.The existing stochastic-approximation mean-square consensus protocols are inevitable to deal with the additive system noises,and the method of Kalman filtering combining with information infusion is not applicable because of its computational complexity.Applying the solution of the algebra Riccati equation and the information of the communication topology,the consensus protocol is designed based on the relative state error.With this protocol,the sufficient conditions are proposed and the consensus error is characterized.Furthermore,the following error is given for the case of leader-follower multi-agent systems.The detailed work is presented in Chapter Ⅱ and Chapter Ⅲ.(2)The mean-square consensus problem for the multi-agent systems with controller-dependent multiplicative noises is considered.By applying the method of matrix decomposition,the consensus problem is translated to a simultaneous stability problem of N-1 subsystems.Combing with a positive solution to a parameterized inequality and the communication structure of multi-agent system,the consensus protocol is designed based on the state error of the agent and its neighbors.Based on the proposed protocol and Lyapunov theory,the simultaneous stability of these N-1 subsystems is to be proved.Hence,the sufficient conditions of consensusability of the multi-agent systems with multiplicative noise is obtained.The detailed work is presented in Chapter Ⅳ.(3)The mean-square constrained consensus problem of the multi-agent systems with both convex set constraint and additive noises.Both discrete-time and continuous-time cases are considered.The methods of weighted average,projection and Ito formula are taken into account to design the consensus protocols.Based on these protocols,it is proved that the multi-agent systems can reach bounded mean-square constrained consensus.The detailed work is presented in Chapter Ⅴ.