Adaptive Fuzzy Finite‐Time States‐Constrained Control for Fractional‐Order Nonlinear Systems

ABSTRACT

This paper investigates the issue of finite‐time states‐constrained control for fractional‐order nonlinear systems. Firstly, unknown nonlinear functions are approximated by using fuzzy logic systems (FLSs). To handle states‐constrained problem, a novel asymmetric tan‐type barrier Lyapunov function (ATBLF) is proposed, which possesses smooth and convex properties, thereby facilitating fractional‐order operations. Secondly, a new switching compensation mechanism composed of piecewise differentiable switching functions and auxiliary functions is developed for constructing virtual and actual controllers. The piecewise differentiable switching function can effectively avoid the common controller singularity issues in sense of finite‐time control. The auxiliary functions are constructed to eliminate the effect of coupling terms generated by the ATBLF. Furthermore, we propose an adaptive fuzzy constrained control strategy utilizing a fractional‐order nonlinear filter. Under appropriate conditions, the finite‐time stability of the closed‐loop system is rigorously proven through fractional‐order Lyapunov stability theory, while ensuring all system states remain within predefined constraint boundaries. Numerical simulations validate the effectiveness of the proposed control method.