Distributed Control Of Stochastic Heterogeneous Multi-Agent Systems

In recent years,the distributed control problem of homogeneous multi-agent systems in perfect communication environments has been widely studied.However,on the one hand,in practical applications,the dynamics of agents are often heterogeneous.On the other hand,when each agent interacts with its neighbors through the communication network,communication processes are inevitably interfered by random noises due to uncertain communication environments.For example,in yaw control of multiple unmanned aerial vehicles,the yaw angles obtained from the preceding vehicles through a communication network are usually interfered by random noises.This involves the distributed control problem of multi-UAV systems with noises,and inspires people to study the distributed control problem of stochastic heterogeneous multi-agent systems.By combining matrix theory,probability theory,stochastic analysis and output regulation theory together,the distributed control problem of stochastic heterogeneous multi-agent systems is studied.The main contribution includes the following points.1.We study cooperative output feedback distributed control of stochastic linear heterogeneous multi-agent systems.Each agent has a continuous-time linear heterogeneous dynamics with incompletely measurable state,and there are additive and multiplicative noises along with information exchange among agents.We propose a set of admissible distributed observation strategies for estimating the leader’s and the followers’ states,and a set of admissible cooperative output feedback control strategies based on the certainty equivalence principle.By output regulation theory and stochastic analysis,we show that for observable leader’s dynamics and stabilizable and detectable followers’ dynamics,if the intensity coefficient of multiplicative noises multiplied by the sum of real parts of the leader’ s unstable modes is less than 1/4 of the minimum non-zero eigenvalue of graph Laplacian,then there exist admissible distributed observation and cooperative control strategies to ensure mean square bounded output tracking,provided the associated output regulation equations are solvable.2.We study the cooperatability of the first-order multi-agent systems consisting of a leader and a follower with multiplicative noises under Markov switching topologies.Each agent has a first-order linear dynamics and there are multiplicative noises along with information exchange among agents.What’s more,the communication topologies are Markov switching topologies.By the stability theory of stochastic differential equations with Markov switching and the Markov chain theory,we give the necessary and sufficient conditions for the cooperatability of the leaderfollowing multi-agent systems.The conditions are as follows.(i)The product of the system’s state parameter and the square of multiplicative noise intensities is less than 1/2.(ii)The transition rate from the mode that the follower is not connected with the leader to the mode that the follower is connected with the leader is greater than two times of the system’s state parameter.(iii)The transition rate from the mode that the follower is connected with the leader to the mode that the follower is not connected with the leader,is less than a constant,which is related to the system’s state parameters,the multiplicative noises intensities and the transition rate from the mode that the follower is not connected with the leader to the mode that the follower is connected with the leader.3.We study cooperative output feedback distributed control of stochastic nonlinear heterogeneous multi-agent systems.Each agent has a continuous-time stochastic nonlinear heterogeneous dynamics with an unmeasurable state,and there are additive and multiplicative noises along with information exchange among agents.Sufficient conditions on the dynamics of agents,the network graph and the noises for the existence of admissible distributed observation and cooperative control strategies are given to ensure mean square bounded output tracking.We show if the dynamics of each agent satisfies the Lipschitz condition,and the product of the leader’s Lipschitz coefficient,the intensity of multiplicative measurement noises,and the constant related to the leader’s Lipschitz coefficient and dimension is less than 1/4 the minimum nonzero eigenvalue of graph Laplacian,then there exist admissible distributed observation and cooperative control strategies to ensure mean square bounded output tracking.4.We study the mean-square bipartite output tracking problem of heterogeneous multiagent systems with communication noises and delays under the signed graph.Each agent has a continuous-time linear heterogeneous dynamics with incompletely measurable state,and there are multiplicative noises along with information exchange among agents.Sufficient conditions on the dynamics of agents,the network graph and the noises for the existence of admissible distributed observation and cooperative control strategies are given to ensure mean square bipartite output tracking.It is proved that for observable leader’s dynamics and stabilizable and detectable followers’ dynamics,if the multiplicative noise intensity,the sum of real parts of the leader’ s unstable modes,the maximum eigenvalue and the minimum non-zero eigenvalue of graph Laplacian and the delay satisfy the corresponding inequality,then there exist admissible distributed observation and control strategies to ensure mean square bipartite output tracking,provided the associated output regulation equations are solvable.