Consensus Stability Research Of Stochastic Multi-Agent Systems

Multi-agent system is ubiquitous in nature but intricate magical phenomenon.In recent years,multi-agent system was paid more and more attention by researchers from all kinds of fields such as control,physics,mathematics,biology,computer,etc.Since the random disturbance is inevitable in the practical multi-agent system,deterministic multi-agent system just is the idealization of the practical multi-agent system,but the stochastic multi-agent system is closer to the real nature.The consensus stability of the stochastic multi-agent systems is the basis of stochastic multi-agent systems research,and the states of the stochastic multi-agent system eventually tend to the same value over time by using stochastic stability theory.In this dissertation,with the help of the existing research results,based on the algebraic graph theory and matrix theory,and by the stochastic stability theory,Markov jump threory and stochastic approaximation theory,several consensus stability problems for the stochastic multiagent system with noises,optimization,varying time-delays and Markovian switching topology are investigated.This provides some new design ideas and effective design effect for the research and extensive application of consensus problems.The main work and contributions of this dissertation are as follows:1)As the consensus stability conditions of stochastic multi-agent system are too conservative,the sufficient condition of the consensus stability conditions is obtained when the consensus gain c(t)of stochastic multi-agent system is a positive constant although the consensus gain c(t)does not meet the gain condition of robust diminishing stochastic approximation.Next we broaden the condition that the consensus-gain function c(t)always must be positive,and obtain the sufficient condition of the consensus stability when the consensus-gain function c(t)is a negative constant.Finally,two simulation examples are given to illustrate the feasibility and effectiveness of the proposed results.2)The stochastic consensus stabilization problems for a stochastic high-order multi-agent system with Markovian switching topologies,stochastic communication noise and unstable open-loop poles are studied.By using probability limit theory,algebraic graph theory,Markov chain theory and stability analysis methods of the continuous-time Markovian jump parameter systems,a necessary and sufficient condition for the continuous-time consensus stability is obtained.The necessary and sufficient condition is that the union of the communication topology set gm ={g(k);1?k?s} contains a spanning tree and that the pair matrix(Ac,Bc)is stabilizable.Finally,a simulation example is given to illustrate the feasibility and effectiveness of the proposed results.3)In view of the reality of which stochastic multi-agent systems in practice is often the discretization of stochastic multi-agent systems,by introducing a parameter(step-size)to discrete-time stochastic multi-agent systems,consensus stabilization problems become more complicated than that in continuous-time systems.By using of a new mathematical tool of the discrete martingale theory,cauchy inequality,and stochastic stability theory,the discrete-time stochastic consensus stabilization problems for stochastic multi-agent systems with linear time-invariant agent dynamics over randomly switching topologies and stochastic communication noises is investigated.The method for designing a consensus gain is important since it allows for separation of the design problem from the graphs.In this view,the design of consensus gain of stochastic multi-agent system and the network topologies are decoupled.This provides the effective rationale for the consensus stability problem of the stochastic multi-agent system subject to Markovian switching topologies and additive disturbances.Finally,a simulation example is given to illustrate the feasibility and effectiveness of the proposed results.4)For stochastic approximation based consensus algorithms with switching topologies,the existing convergence analysis methods may be difficult to guarantee for switching digraphs because these techniques heavily relies on quadratic Lyapunov functions or Razumikhin functions.To overcome the inherent limitations of the existing methods,we develop a new stochastic approximation and ergodicity approach for backward products of degenerating stochastic matrices via a discrete time dynamical system approach to analyze the consensus stability problem of stochastic multi-agent systems with noises,Markovian switching topology,and communication delays;and the necessary and sufficient condition of the consensus stability is that the sequence of stochastic matrices A(k)is ?(k)-compatible.The controller design and consensus stability of stochastic multi-agent systems with noises,Markovian switching topology,and communication delays are solved effectively.Finally,a simulation example is given to illustrate the feasibility and effectiveness of the proposed results.5)For applications often have to consider the minimum communication cost,minimum energy consumption or investment income maximization and so on,given the performance index of the stochastic multi-agent systems,the optimal controller of the high order stochastic multi-agent with Markovian switching topology and random noise is designed by using the dynamic programming principle of stochastic optimal control.Then the stability of stochastic multi-agent system with the distributed optimal control is analyzed.Finally,a simulation example is given to illustrate the feasibility and effectiveness of the proposed results.