G-Brownian Motion-Based Dynamics Of Multi-Agent Systems

As an important branch of system control and artificial intelligence,cooperation control of multiagent system is widely used in multi-spacecraft formation,multi-satellite exploration and so on.As a basis of system cooperation for multi-agent,the consensus control has attracted close attention of many experts and scholars.Due to the universal existence of external disturbance and time delays,it is more practical to investigate the multi-agent systems after introducing some random factors.On the basis of existing results on consensus problem for stochastic multi-agent systems,the consensus of multi-agent systems with random vibration which obeys G-normal distribution is further investigated in this thesis.The main work can be divided into four chapters and organized as follows:In the first chapter,the significance and research background of the consensus problem of stochastic multi-agent systems,prerequisites and notation together with current research situation of G-Brownian motion are briefed.Then the main contents of this dissertation are also expounded.The second chapter investigates the consensus problem related to the multi-agent system with random vibration which obeys G-normal distribution.Based on the fixed topology and distributed coordinated control,state feedback controller is designed.In Section 2.1,mean-square consensus is firstly considered for the model in which the stochastic term is independent of the state value of the agent.Some criteria are obtained by using the expressions of solutions.And for the model in which the stochastic term relies on the state of the agent,some sufficient conditions for mean-square consensus are derived by using the G-It?o formula and the Lyapunov function method.In Section 2.2,for the case where the stochastic term is independent of the agent state value,the Markov inequality and the exponential martingale inequality are put forward to handle quasi-sure consensus of the system in which the control gain function only exists in the stochastic term.Next the second system model in Section 2.1 can be proved to reach quasi-sure consensus under given criteria by using the Markov inequality and some properties related to G-expectation.In the last,numerical examples are given to show the effectiveness of the conclusion.In the third chapter,the consensus control of stochastic multi-agent systems with fixed time delays is further studied on the basis of the previous chapter.In Section 3.1,mean-square consensus of systems with the fixed time delays only in deterministic or stochastic terms are addressed.Several sufficient conditions are obtained by the differential resolvent function,method of variation of constant and Lyapunov theorem.In Section 3.2,the quasi-sure consensus of the first model is analyzed according to the existing conclusion in Section 2.2.Then properties of mean-square consensus,G-expectation and Markov inequality are used to yield sufficient conditions for the second system to achieve the quasi-sure consensus.Finally,numerical examples are given to verify the effectiveness of the conclusions in this chapter.In the last chapter,a summary has been done for all discussions in the dissertation.Several promising topics are further presented for the consensus problem of the stochastic multi-agent systems.