Adaptive Fuzzy Iterative Learning Control of Constrained Systems With Arbitrary Initial State Errors and Unknown Control Gain

Abstract

An adaptive fuzzy iterative learning control(AFILC) method is presented to address the state tracking issue of constrained systems with arbitrary initial state errors and unknown control gain. A novel desired error trajectory is systematically developed in the polynomial form to relax the identical initial condition, which allows for arbitrary setting of initial values for all the system state errors. The proposed desired error trajectory can also relax the iteration-invariance restriction on the reference signals due to the independence of the reference trajectories. An asymmetric integral fractional barrier Lyapunov function is developed, keeping the tracking error within the preassigned boundary. Moreover, there is no need to estimate the unknown control gain function in the controller design, reducing computation burden. Numerical simulations and experiments in the permanent magnet synchronous motor experimental platform are provided to illustrate the efficacy of the proposed method. Note to Practitioners—Most practical systems often perform repetitive tasks in industrial processes, such as the repetitive handling process of manipulators, and the rotation process of motors, etc. Iterative learning control method is model independent, and fully utilizes the repetitive characteristics during system operation. However, due to irregular initial state drifts caused by locating operations at different iterations, the identical initial condition is often violated in practical iterative learning control applications. This paper presents an adaptive fuzzy iterative learning control method to address the state tracking issue of constrained systems with arbitrary initial state errors and unknown control gain. The problem of inconsistent initial values is addressed by designing a desired error trajectory in the polynomial form, such that arbitrary setting of initial values for all the system state errors is allowed. For safe operation in practice, an asymmetric integral fractional barrier Lyapunov function is developed to keep the tracking error within the preassigned boundary. The satisfactory experimental results on the permanent magnet synchronous motor experimental platform also demonstrate the practical effectiveness of the proposed method.