Fixed-Time Prescribed Performance Unknown Direction Control of Discrete-Time Non-Affine Systems Without Nussbaum-Type Function
Xiangwei Bu, Humin Lei
Abstract
In this article, we concern on prescribed performance autonomous control of discrete-time non-affine systems subject to unknown nonlinearities and directions. Unlike existing Nussbaum-type function based strategies, the addressed issue is transformed as the unknown direction control of affine systems, and it is further effectively handled without using such Nussbaum-type functions within a novel design framework that is completely different from current sliding-mode-based structure. Inside the newly developed framework, we devise a family of fixed-time performance functions and then define discrete-time nonlinear functions for control synthesis. On this basis, a new indirect stabilization approach is achieved, to pursue desired prescribed performance in the discrete-time domain with sliding-mode-design avoidance. Besides, adaptive neural approximations are employed to reject system unknown nonlinearities, and improved adaptive laws are explored to reduce computational load. Finally, we apply the proposed method to a type of discrete-time systems to verify its effectiveness and improvement. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The motivation of this article arises from the need for fixed-time prescribed performance autonomous control of discrete-time systems exhibiting unknown directions. However, existing discrete-time PPC methodologies, constructed within the sliding-mode-based framework, cannot guarantee the fixed convergence time for tracking errors. To address this issue, we firstly propose a new family of discrete-time performance functions which impose fixed convergence time for tracking errors in the discrete-time domain, and then we further develop a new design framework which is completely different from current sliding-mode-based structure. On those bases, we also cleverly handle the unknown direction control problem without utilizing Nussbaum-type functions. The presented results of this paper are of great significance for providing a standard and general procedure for discrete-time PPC development.