Semi-globally/globally stable adaptive NN backstepping control for uncertain MIMO systems with tracking accuracy known a priori

Abstract

This paper focuses on the problem of direct adaptive neural network (NN) tracking control for a class of uncertain nonlinear multi-input/multi-output (MIMO) systems by employing backstepping technique. Compared with the existing results, the outstanding features of the two proposed control schemes are presented as follows. Firstly, a semi-globally stable adaptive neural control scheme is developed to guarantee that the ultimate tracking errors satisfy the accuracy given a priori, which cannot be carried out by using all existing adaptive NN control schemes. Secondly, we propose a novel adaptive neural control approach such that the closed-loop system is globally stable, and in the meantime the ultimate tracking errors also achieve the tracking accuracy known a priori, which is different from all existing adaptive NN backstepping control methods where the closed-loop systems can just be ensured to be semi-globally stable and the ultimate tracking accuracy cannot be determined a priori by the designers before the controllers are implemented. Thirdly, the main technical novelty is to construct three new nth-order continuously differentiable switching functions such that multiswitching-based adaptive neural backstepping controllers are designed successfully. Fourthly, in contrast to the classic adaptive NN control schemes, this paper adopts Barbalat׳s lemma to analyze the convergence of tracking errors rather than Lyapunov stability theory. Consequently, the accuracy of ultimate tracking errors can be determined and adjusted accurately a priori according to the real-world requirements, and all signals in the closed-loop systems are also ensured to be uniformly ultimately bounded. Finally, a simulation example is provided to illustrate the effectiveness and merits of the two proposed adaptive NN control schemes.