Event-Triggered Adaptive Fuzzy PI Control of Uncertain Fractional-Order Nonlinear Systems With Full-State Constraints

This article is devoted to the adaptive fuzzy proportional-integral (PI) control of uncertain fractional-order (FO) strict-feedback nonlinear systems subject to full-state constraints (FSCs) and external disturbances via an event-triggered (ET) control technique. First, fuzzy logic systems are introduced to approximate unknown nonlinear functions. Second, a novel adaptive FOPI controller with a simple structure and low calculation cost is developed, and it is able to determine its PI gains adaptively and automatically without involving manual operation or trial and error procedures, which is an improvement compared with the traditional PI control scheme. Third, a relative-threshold-based ET controller is constructed so that the communication load from the controller to the actuator can be significantly decreased, and there is no Zeno behavior. Then, a barrier Lyapunov function is introduced into the backstepping recursive process to avoid FSC violations. Moreover, all closed-loop signals are bounded, and the output is driven to follow the desired output through the FO Lyapunov stability analysis. In particular, the proposed approach does not require a priori knowledge of the FO derivative of the reference signal. Finally, the feasibility of the proposed scheme is verified by numerical simulations.