Distributed Containment Control And Application Of Uncertain Fractional-order Multi-agent Systems

The distributed containment control problem of multi-agent systems is a class of typical collaborative control problem,where all agents are required to move into the convex hull spanned by multiple leaders asymptotically.For some phenomena with memory and heredity,the dynamics of agents can be better described by fractional-order calculus.This paper mainly studied the distributed containment control of various uncertain fractional-order multi-agent systems.Specifically:1.The quasi-containment control problem of fractional-order multi-agent systems is solved via event-triggered control mechanism.Only the information at the trigger moment is used by the event-triggered mechanism.Besides,some sufficient conditions are deduced for achieving quasi-containment control,it is proved that the event triggering interval has a strictly positive lower bound,which theoretically guarantees that the Zeno behavior can be avoided.2.The containment control problem of fractional-order multi-agent systems under un-constraint and nonconvex constraints is investigated.Firstly,based on projection operator,distributed containment control protocol is designed for each agent.The L₁interpolation approximation technology is used to deal with the projection operator,and the closed-loop system is transformed into the corresponding equivalent system.Further,by using the prop-erties of convex set and Mittag Leffler function,the stability of the system is analyzed.It is proved that all followers would asymptotically converge into the convex hull formed by multiple leaders,and the control input or state of all agents are constrained to lie in their respective nonconvex constraint sets.3.The containment control problem of fractional-order multi-agent systems with un-known nonlinear function and external disturbances is investigated.On the one hand,for fractional-order multi-agent systems with unknown nonlinear function,the radial basis func-tion neural network is used to approximate the unknown nonlinear function,and the adaptive distributed containment control protocol is designed.Then,sufficient conditions for achiev-ing containment control are obtained by using the properties of Mittag-Leffler function.On the other hand,the containment control of fractional-order multi-agent systems with model errors and external disturbances is investigated.Based on its equivalent state space model,the linear matrix inequality condition is derived for achieving containment control under the robust H_?performance.4.The containment control problem of multi-agent systems with fractional Brownian motion disturbances is investigated.Assuming that the Hurst index of the fractional Brownian motion H?(0.5,1).A state observer is designed for each follower to estimate the leader's information.Then,it is proved that the agent system can realize the containment control in the sense of exponential mean-square.Furthermore,by weakening the limitation of the noise intensity matrix operator,using the properties of the analytic semigroup and the fixed-point theorem,a new control function is defined.It is proved that the multi-agent systems could achieve the mean-square quasi-containment control.