Adaptive Fuzzy Reinforcement Learning‐Based Optimal Backstepping Control for Fractional‐Order Nonlinear Systems With Full‐State Constraints and Input Saturation

This paper presents an adaptive fuzzy backstepping control approach utilizing reinforcement learning (RL) for fractional‐order (FO) strict‐feedback nonlinear systems with full‐state constraints and input saturation. The RL‐based identifier‐critic‐actor architecture is constructed via fuzzy logic systems (FLSs), which is applied to induce the approximate optimal controller. The proposed RL algorithm not only ensures rapid convergence of the adaptive updating weight parameters, but also removes the rigorous requirement for parameter adaptation under persistent excitation condition. Compared to the classic gradient descent method for training the weight update laws of FLSs, the proposed scheme simplifies the computational complexity. An improved FO filter is introduced to overcome the “complexity explosion” problem caused by the traditional backstepping designs. A barrier Lyapunov function is introduced at each step of the recursive process to avoid states exceeding the desired constraints. According to the FO Lyapunov stability theory, it is proven that all states remain within the required constraints and that all closed‐loop signals are bounded. The feasibility of the presented algorithm is further verified through comparative simulation.