Adaptive prescribed performance control for nonlinear pure-feedback systems: a scalarly virtual parameter adaptation approach

Abstract

In this paper, an adaptive prescribed performance controller, consisting of a novel scalarly virtual parameter adaptation (SVPA) technique, is developed for a class of single-input and single-output high-order nonlinear pure-feedback systems in the presence of model uncertain yet locally Lipschitz nonlinearities. The objective of this work is to improve the transient and steady performance of pioneering prescribed performance control (PPC) by incorporating a single SVPA mechanism into the virtual and actual controllers, therein, the unknown yet bounded parameters are defined with respect to proper composite system and virtual functions, bringing the gap between pioneering PPC and linearly parameterized approximator-based PPC schemes (including neural networks, fuzzy logic systems, etc.), that is, the computational complexity of proposed method exceeds PPC with one level (caused by introduced single adaptive law) yet maintains low level with comparison to linearly parametrized approximator-based PPC. It is guaranteed that both virtual and actual tracking errors converge transiently to small residual sets characterized by prescribed performance functions and control parameters simultaneously and ultimately converge to zero, which is also proved by rigorously mathematical analysis using Lyapunov stability theorem. The closed-loop signals are kept globally ultimately uniformly bounded, and comparative simulation results are presented to demonstrate the effectiveness and advantages of the theoretical findings.