Data-driven-based Predictive Optimal for a class of Iterative Learning Control by Q-learning method

The paper investigates predictive optimal for P-type iterative learning control (lLC) under unknown system's dynamic. First, with an Δuk+l-based discounted linear quadratic cost function of control errors in ILC, we formulate the predictive optimal problem for P-type ILC and present a solution for such a problem in a discrete algebraic Riccati equation (DARE) with known system's dynamic, by which a predictive optimal algorithm can be established. Second, a reinforcement Q-Iearning method is proposed to find predictive optimal solution for P-type ILC under unknown system's dynamic, which is intended to develop a model-free and iterative learning algorithm to implement ILC with a higher convergence speed only by utilizing the input and output data of ILC. Based on the performance function, a Q-function is elaborately chosen in an iterative formulation with trials of Δuk+l and control errors for critic P-type ILC performance with its updated converge rated. Third, the convergence of the algorithm is proved and discussed with it conditions. Last, an illustrative digital simulation at MATLAB verifies the effectiveness of the proposed algorithm and shows its advantages over the traditional method.