Fuzzy Weight-Based Reinforcement Learning for Event-Triggered Optimal Backstepping Control of Fractional-Order Nonlinear Systems

Fractional-order nonlinear systems have been widely studied, and their optimal control problems have been difficult to be solved. In this article, an event-triggered fuzzy reinforcement learning method is proposed to achieve the optimal control of fractional-order nonlinear systems. First, the fractional Hamiltonian–Jacobi–Bellman equation is derived by constructing an equivalent integer-order auxiliary system and the fractional optimal solution under a global performance index is derived. Then, two fuzzy logic systems are used to form an actor–critic structure to approximate the cost function and the optimal controller, respectively. By constructing the Lyapunov function of the optimal fuzzy weight error, the fractional weight learning laws are designed to ensure that the fuzzy weights converge to the optimum. With this approach, it is not necessary to train the fuzzy weights by gradient descent, and the persistent excitation condition is relaxed. Considering reducing the computational burden, an event-triggered mechanism is used to avoid Zeno behavior. Finally, the effectiveness of the algorithm is verified by stability analysis and simulation.