Formation Control Problem Of Fractional-order Multi-agent Systems

Multi-agent formation control problem is an extension of multi-agent systems con-sensus problem,and is applied widely in the fields of control science and engineering,system science,information and communication engineering and so on.It has attract-ed the attention of domestic and foreign scholars.In this paper,the formation control problem of multi-agent systems with virtual leader is considered in finite time interval under the repeatable running environment,as well as the following achievement have been accomplished:(1)For linear time-invariant fractional multi-agent systems with control for systems input,designed P type and PI type learning law under the fixed directed topology graph;f'or system without control for systems input,designed PD? type learning law under the fixed directed topology graph and the iteration-varying switch directed topology graph respectively,synthetically applying to Holder inequality and contracting mapping principle,some sufficient conditions are presented to ensure error of multi-agent systems convergence to 0 on finite time interval in the sense of proper norm.That is the output trajectory of followers can track the trajectory ofvirtual leader in finite time interval.(2)For nonlinear time-invariant fractional multi-agent systems with control for sys-tems input,designed P type and pI? type learning law under the fixed directed topolo-gy graph and iteration-varying switch directed topology graph respectively;for systems without control for systems input,designed PDO type learning law under the fixed di-rected topology graph,synthetically applying to Lipschitz condition,Holder inequality,Gronwall inequality and contracting mapping principle and so on.The sufficient con-dition which the tracking error of multi-agent systems convergence to 0,is presented in finite time interval in the sense of'the corresponding norm.It shows that the output trajectory of followers can track the trajectory of virtual leader in finite time interval.Last,the validity and effectiveness of all theoretical results are verified through numerical examples.