Adaptive NN control for nominal backstepping form with periodically time‐varying and nonlinearly parameterized switching functions

Abstract

In this paper, the prescribed tracking performance control problem is addressed for uncertain nonlinear systems with unknown periodically time‐varying parameters and arbitrary switching signal. By utilizing radial basis function neural network and fourier series expansion, an approximator is developed to overcome the difficulty of identifying unknown periodically time‐varying and nonlinearly parameterized functions. To achieve the ideal tracking control performance and eliminate the influence of filtering error, a novel command filter‐based adaptive neural network prescribed tracking performance controller is designed by introducing a filtering compensation mechanism. Differently from the standard Backstepping technique, the proposed control scheme eliminates the “explosion of complexity” problem and relaxes the constraint condition on the reference signal. And then, it is warranted that the closed‐loop system is semi‐globally ultimately uniformly bounded and the tracking error is always limited to the specified region bounded by the performance functions. Three simulation examples are used to demonstrate the feasibility of the developed technique in this paper.