Predefined-time adaptive learning control of nonlinear strict-feedback systems via dynamic regressor extension and mixing

Abstract

This paper develops a parameter identification algorithm and a novel adaptive tracking control strategy for a specific group of nonlinear strict-feedback systems incorporating the concept of predefined time under model uncertainties. A three-layer transformation-based parameter estimation method with predefined-time convergence properties is proposed to relax the strict persistent excitation condition imposed by conventional approaches. The singular terms that may occur in traditional backstepping design procedures are avoided by using a hyperbolic tangent function to design new control laws and filters. Composite learning control approach that incorporates the algorithm for parameter identification into the framework for adaptive dynamic surface control can achieve error convergence within a practical predefined time. By using Lyapunov analysis, the semi-global uniformly predefined-time boundedness for the closed-loop dynamics is demonstrated. Numerical experiments demonstrate the viability of developed control scheme.

Keywords: Adaptive control; Backstepping control; Nonlinear strict-feedback system; Predefined-time control.