Adaptive Fuzzy Control for T-S Fuzzy Fractional Order Nonautonomous Systems Based on Q-learning

In this article, fractional-order nonautonomous system (FONAS) with the input delay and nonlinear terms are considered and investigated using adaptive fuzzy control method based on Q-learning. With the novel estimation model, the defined predictions for the error system determines the weights of the fuzzy logic system (FLS). On this basis, an error derivative-based cost function is introduced, which not only deals with the classic problem that quadratic term cost function is unbounded in infinite time, but also resolves the challenge that the exponential discount factor cost function fails to stabilize asymptotically. For the unmeasurable part of the state, the designed fuzzy observer eliminates the restriction on the gain parameters. Furthermore, based on the measured information and the actor–critic architecture of the online training FLSs, the improved adaptive fault-tolerant control (FTC) input approximate the optimal control. Utilizing a fractional-order Lyapunov method, the stability of FONAS with actuator faults is discussed, and a sufficient criterion for stability is obtained, which is easier to perform with convex optimization tools. Finally, numerical simulations are shown to display the effectiveness of the optimal adaptive fuzzy FTC strategy.