Adaptive Neural Network Iterative Learning PI Control of Fractional-Order Nonlinear Systems Using Generalized Barrier Lyapunov Function

Note that the available barrier Lyapunov function (BLF) design considers that the precondition of the specified function must be a smooth convex function, which is relatively harsh for most models. In this article, built on proportional-integral (PI) theory, an adaptive neural network (ANN) PI iterative learning tracking control method for fractional-order nonlinear systems (FONSs) with full-state constraints is presented. A new type of BLF is built that only requires finding a derivative of this function needs to be monotonic under the fractional Lyapunov direct method. To meet the needs of reducing computational complexity and data volume, the designed backstepping controller based on PI control consists of a series of constant gains and dynamic variables with basic linkage relationships. Moreover, it also incorporates iterative learning algorithm that can achieve continuous or discontinuous self-learning and updating. The results indicate that all closed-loop signals of FONSs are semi-globally ultimately uniformly bounded and the constraint is not violated. Theoretical analysis and numerical simulation have verified the rationality of this study.