Adaptive multi-dimensional Taylor network tracking control for time-varying delay nonlinear systems with unmodeled dynamics and input saturation

This paper is concerned with the adaptive multi-dimensional Taylor network (MTN) tracking control problem of a class of nonlinear systems simultaneously characterized by time-varying delays, unmodeled dynamics, and input saturation. The Lyapunov-Krasovskii functions are constructed to cope with the effect of time-varying delay. A dynamic signal is designed to address the unmodeled dynamics in the backstepping procedure. The input saturation is transformed into a linear model with bounded errors by using a Gaussian error function. Meanwhile, an adaptive tracking control method is designed by combining the MTN approximation technology with the backstepping method to handle the unknown nonlinearities within the controlled system. The proposed control method boasts a simple structure and reduced computational complexity. Furthermore, based on Lyapunov stability theory, it is demonstrated that all signals in the closed-loop system remain bounded, and the system tracking errors converge to a small domain near the origin. Ultimately, the effectiveness of the proposed control strategy is substantiated through two representative simulation examples.