Predefined-Time Adaptive Neural Tracking Control of Switched Nonlinear Systems

This article investigates the neural-network-based adaptive predefined-time tracking control problem for switched nonlinear systems. Neural networks are employed to approximate the unknown part of nonlinear functions. The finite-time differentiators are introduced to estimate the first derivative of the virtual controllers. Then, a novel adaptive predefined-time controller is proposed by utilizing the backstepping control technique and the common Lyapunov function (CLF) method. It is explained by the theoretical analysis that the developed controller guarantees that all signals of the switched closed-loop systems are bounded under arbitrary switchings and the tracking error converges to zero within the predefined time. A simulation is shown to verify the validity of the developed predefined-time control approach.

I. Introduction

Switched systems as a special category of hybrid systems are composed of a certain number of subsystems and a switching signal. As known to us all, many systems can be modeled as switched systems in practical applications, such as aircraft control systems, electrical systems, and robot manipulators. Adaptive backstepping control is able to adjust parameters by online learning, so it as an efficient control scheme is extensively applied to design controllers of switched systems. Recent years, many prominent scholars have made a profound study on the switched systems and achieved many meaningful results [1], [2], [3], [4]. To list a few, the issue of adaptive stabilization for a category of uncertain switched nonlinear systems has been taken into account in [1]. The adaptive tracking controllers were designed for a category of uncertain switched systems under arbitrary switchings in [2]. A common Lyapunov function (CLF) method was proposed for the study of switched systems in the landmark work [5]. In addition, a multiple Lyapunov function method, average dwell-time scheme, and other methods are also mentioned in [5]. As we know, when all subsystems have a CLF, the switched systems can remain stable under arbitrary switching. Hence, CLF as a useful tool is widespreadly applied to control synthesis of switched linear systems [6], [7], [8], and lately extends to deal with the global stabilization issue for switched nonlinear systems, see [9] and [10].