Consensus Control For Fractional-order Discontinuous Multi-agent Systems

Compared with the single agent,the multi-agent systems can complete the tasks more effectively,improve the fault tolerance and robust,and have higher flexibility.Therefore,the multi-agent systems have been widely applied in the field of control and artificial intelligence.Particularly,the consensus research for fractional-order multi-agent systems has attracted many attention from the scholars.Recently,there have been lots of results on the continuous fractional order multi-agent systems.In this paper,the fractional order multiagent systems with discontinuous inherent dynamics functions are investigated,and the specific research contents are as follows:Firstly,based on the undirected topology,agents are divided into several groups.When the inherent dynamics functions are discontinuous and nondecreasing,under/without the inter-group balance condition,two new distributed control protocols are designed,respectively.By applying Lyapunov stability theory and Clarke's nonsmooth analysis techniques,and designing Lur'e Postnikov-type Lyapunov functional,the global Mittag-Leffler group consensus conditions are established in the form of linear matrix inequalities.Secondly,under the assumption that the inherent dynamics functions are subject to the local H ?lder nonlinear growth,the Lyapunov functional including the variable upper limit integral item,which is related to the internal dynamics functions,is constructed.Based on the designed distributed control protocols,the global group consensus conditions in finite time are achieved in terms of linear matrix inequalities.Moreover,the settling time of finite-time group consensus is estimated.Finally,for the fractional order multi-agent systems with singular perturbation,by utilizing the event-triggered control strategy and the row-switching elementary transformation properties of matrices,based on the designed event-triggered control protocol,the global Mittag-Leffler leader-following consensus control conditions are given in the form of matrix inequalities.And the tracking speed can be predefined.