Adaptive Finite-Time Tracking Control for Nonlinear Time-Varying Delay Systems With Full State Constraints and Input Saturation

Tian Xu,Yuxiang Wu

doi:10.1109/access.2021.3112179

Abstract

This paper investigates the adaptive finite-time tracking control problem for a class of nonlinear time-varying delay systems subject to full state constraints and input saturation. The nonlinear state-dependent functions (NSDFs) are introduced to handle the asymmetric time-varying full state constraints without feasibility conditions. To cope with the unknown time-varying delays, the radial basis function neural networks (RBF NNs) and the finite covering lemma are utilized. Avoiding the use of the Lyapunov-Krasovskii functionals (LKFs), no restriction on the derivative of the time-varying delays is needed. Meanwhile, the effect of the input saturation is eliminated by the augmented function with an auxiliary control signal. The adaptive finite-time tracking controller with only one adaptive parameter is constructed by applying the command filter approach and backstepping technique. It is proved that the proposed controller can ensure that all signals in the closed-loop system are bounded and the tracking error converges to a small neighborhood of the origin in a finite time. Finally, the effectiveness of the proposed scheme is demonstrated by two simulation examples.

Highlights

In control theory, the existence of time delays may degrade the stability of the systems and give rise to the difficulties of control design
Fuzzy logic systems (FLSs) and NNs have been widely used to approximate the uncertain functions in the adaptive control design [5,6,7]
By combining NNs or fuzzy logic systems (FLSs) with Lyapunov-Krasovskii functionals (LKFs), several adaptive tracking control schemes were proposed for nonlinear strictfeedback systems with constant time delays in [9,10,11]

Summary

INTRODUCTION

The existence of time delays may degrade the stability of the systems and give rise to the difficulties of control design. To the best of our knowledge, the adaptive finite-time tracking control problem has not been fully studied for nonlinear time-varying delay systems with full state constraints and input saturation. Motivated by the above discussion, this paper aims to design an adaptive finite-time tracking control method for the nonlinear time-varying delay systems in presence of full state constraints and input saturation. Without imposing any assumptions on the derivative of time-varying delays, an adaptive finite-time tracking controller was designed for nonlinear full-state constrained systems with unknown time-varying delays and input saturation.

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Conclusion