Distributed tracking of heterogeneous nonlinear fractional-order multi-agent systems with an unknown leader

By applying the fractional Lyapunov direct method, this paper investigates the distributed tracking problem of nonlinear fractional-order multi-agent systems subject to heterogeneous control gains and a time-varying leader whose input is unknown and bounded over a general directed graph. Due to the existence of heterogeneous control gains as well as a time-varying unknown leader in the nonlinear systems, the fractional-order dynamics of each agent is in essence heterogeneous. At first, a discontinuous distributed controller is constructed to guarantee that the distributed tracking control problem can be solved if some conditions are satisfied. Next, a continuous distributed controller is further proposed to eliminate the undesirable chattering phenomenon of the discontinuous controller, where the upper bound of the tracking error is uniformly bounded and can be made small enough by choosing the parameters appropriately. Finally, some simulation examples are presented to verify the effectiveness of the main results.