Adaptive robust tracking control for uncertain nonlinear fractional-order multi-agent systems with directed topologies

This paper addresses the robust consensus tracking problem for a class of uncertain nonlinear fractional-order multi-agent systems (FOMASs) under general directed topologies. More specifically, FOMASs in the presence of heterogeneous unknown nonlinearities and external disturbances are considered in this paper, which include the second-order MASs as its special cases. First, we design two distributed saturated observers to overcome the deficiency of the traditional tracking control strategies. Second, when there exists a dynamics leader with unknown and bounded state trajectory, a discontinuous observer-based distributed controller with σ-modification adaptive schemes is presented to guarantee the tracking error converges to zero asymptotically. Next, a continuous observer-based distributed controller is further proposed, under which the consensus tracking error is uniformly ultimately bounded (UUB) and can be reduced as small as desired. A neural network (NN), whose weights are tuned online, is used in the designed controllers to approximate the unknown nonlinearities. Motivated by the σ-modification adaptive method, all the proposed adaptation algorithms require only local information and allow for robust even in the presence of heterogeneous unknown disturbances and fractional-order dynamics. Finally, the simulation results validate the efficacy of our proposed method.