Fixed-Time Tracking Control for State-Constrained Nonstrict-Feedback Systems Without Feasibility Conditions

Abstract

This paper investigates the fixed-time tracking control schemes for a class of state-constrained nonstrict-feedback nonlinear systems without involving the feasibility conditions. Based on nonlinear mapping, a nonlinear state transformation function is constructed to convert the constrained system into an equivalent system without state constraints, which achieves the asymmetric time-varying state constraints and eliminates the feasibility conditions on the virtual controllers. A nonlinear fixed-time filter with dynamic surface control is utilized to handle the problem of explosion of complexity in the backstepping framework. Furthermore, we develop a fixed-time observer-based tracking control strategy for the nonstrict-feedback system subject to unmeasured states. To remove the restrictive assumptions of known control gain functions, the nonlinear system is reconstructed and the neural networks are employed to approximate the unknown terms. In addition, a hyperbolic tangent function is utilized to address the input saturation problem. Through the Lyapunov theorem, the closed-loop system is proven to be practical fixed-time stable within the constraint requirements. Finally, simulation results demonstrate the effectiveness of the proposed methods.