Adaptive neural network finite-time tracking control for a class of high-order nonlinear multi-agent systems with powers of positive odd rational numbers and prescribed performance

Abstract

Abstract This paper addresses the adaptive finite-time consensus tracking problem for high-order nonlinear multi-agent systems (MASs) with powers of positive odd rational numbers under prescribed performance. Since the virtual and actual control parts of the dynamics of each follower agent are power functions containing positive odd rational numbers, the method of adding a power integrator is used to overcome the controller design difficulties caused by the power functions. With the aid of a finite-time performance function (FTPF) and neural networks (NNs), a distributed adaptive finite-time consensus tracking controller with prescribed tracking performance is properly designed by the backstepping process. It is shown that the proposed control strategy can guarantee that the consensus tracking error converges to an arbitrarily small neighborhood around zero at any settling time, while all signals of the closed-loop system are semi-globally practical finite-time stable (SGPF-stable). Finally, a simulation example is presented to demonstrate the effectiveness of the proposed method.