Differential evolution-based parameter estimation and synchronization of heterogeneous uncertain nonlinear delayed fractional-order multi-agent systems with unknown leader

In this paper, under a fixed directed graph, the distributed cooperative synchronization of heterogeneous uncertain nonlinear chaotic delayed fractional-order multi-agent systems (FOMASs) with a leader of bounded unknown input is investigated, where the fractional orders and system parameters are uncertain and the controller gains are heterogeneous due to imperfect implementation. It should be noted that the study is more general by considering the FOMASs with time delays, unknown leader, heterogeneity, and unknown nonlinear dynamics. Firstly, a differential evolution-based parameter estimation method is proposed to identify the uncertain parameters. Then based on the identified parameters, by using the matrix theory, graph theory, fractional derivative inequality, and comparison principle of linear fractional equation with delay, a heterogeneous discontinuous controller is designed to achieve the distributed cooperative synchronization asymptotically. Thirdly, a heterogeneous continuous controller is further constructed to suppress the undesirable chattering behavior, where uniformly ultimately bounded synchronization tracking errors can be achieved and tuned as small as desired. Finally, numerical simulations are provided to validate the effectiveness of the proposed parameter estimation scheme and the designed control algorithms.