Adaptive Fuzzy Control Without Feasibility Conditions for Fractional-Order Nonlinear State-Constrained Systems: A Bounded Virtual Controller Design Method

This paper addresses adaptive fuzzy tracking control for fractional-order nonlinear systems (FONSs) subject to asymmetric state constraints without imposing separate feasibility conditions on intermediate virtual controllers. Fuzzy logic systems are used to approximate the unknown nonlinear functions. By exploiting the boundedness of the hyperbolic tangent function, a coordinate transformation and an asymmetric fractional barrier Lyapunov function (AFBLF) are developed to construct bounded virtual control signals. Within a backstepping framework, an adaptive fuzzy controller is designed. Fractional-order Lyapunov analysis establishes semi-global uniform ultimate boundedness of all closed-loop signals and preservation of the prescribed asymmetric constraints. Comparative and benchmark simulations demonstrate constraint satisfaction, moderate control effort, and suppression of high-frequency chattering-like oscillations.