Adaptive Containment Control for Fractional-Order Nonlinear Multi-Agent Systems With Time-Varying Parameters

Abstract

This paper investigates adaptive containment control for a class of fractional-order multi-agent systems (FOMASs) with time-varying parameters and disturbances. By using the bounded estimation method, the difficulty generated by the time-varying parameters and disturbances is overcome. The command filter is introduced to solve the complexity problem inherent in adaptive backstepping control. Meanwhile, in order to eliminate the effect of filter errors, a novel distributed error compensating scheme is constructed, in which only the local information from the neighbor agents is utilized. Then, a distributed adaptive containment control scheme for FOMASs is developed based on backstepping to guarantee that the outputs of all the followers are steered to the convex hull spanned by the leaders. Based on the extension of Barbalat's lemma to fractional-order integrals, it can be proven that the containment errors and the compensating signals have asymptotic convergence. Finally, three simulation examples are given to show the feasibility and effectiveness of the proposed control method.