Adaptive prescribed-time parameter estimation and control for a class of uncertain nonlinear systems

Abstract

This paper presents a prescribed-time (PT) parameter estimation and control algorithm for a class of uncertain nonlinear systems. Using a time-varying forgetting factor and a normalization technique, a two-filter-based parameter estimation error reconstruction mechanism is developed. On the basis of this, a novel PT parameter estimation method is proposed, under the sufficient excitation condition, which is less conservative than the persistency of excitation condition. Furthermore, by combining the proposed PT parameter estimation method and the sliding mode control method, an adaptive PT control law is designed, which makes both the tracking error and the parameter estimation error converge to zero in a prescribed time, while all the closed-loop signals remain bounded. Moreover, a modified adaptive PT control scheme is proposed to avoid any numerical problems that may arise in the implementation of the adaptive PT control method due to the use of the infinity gain function. Finally, the effectiveness of the proposed algorithm is illustrated by two simulation examples.