Neural-Network-Based Finite-Time Bipartite Containment Control for Fractional-Order Multi-Agent Systems

This article focuses on the adaptive bipartite containment control problem for the nonaffine fractional-order multi-agent systems (FOMASs) with disturbances and completely unknown high-order dynamics. Different from the existing finite-time theory of fractional-order system, a lemma is developed that can be applied to actualize the aim of finite-time bipartite containment for the considered FOMASs, in which the settling time and convergence accuracy can be estimated. Via applying the mean-value theorem, the difficulty of the controller design generated by the nonaffine nonlinear term is overcome. A neural network (NN) is employed to approximate the ideal input signal instead of the unknown nonaffine function, then a distributed adaptive NN bipartite containment control for the FOMASs is developed under the backstepping structure. It can be proved that the bipartite containment error under the proposed control scheme can achieve finite-time convergence even though the follower agents are subjected to completely unknown dynamic and disturbances. Finally, the feasibility and validity of the obtained results are exhibited by the simulation examples.