Data-based optimal learning control minimizing performance indexes throughout iterative processes

This paper is aimed at addressing a class of data-based design and analysis problems of optimal iterative learning control (ILC), where the performance index consists of the quadratic terms of the input updating and tracking error over all iterations and time steps. The optimal ILC design is proposed based on the Bellman optimality equation and the convergence analysis of optimal ILC is implemented such that the performance index throughout the whole iterative process is minimized and the perfect tracking objective of ILC is monotonically achieved at an exponential speed. An iterative method for solving the learning gain of optimal ILC is presented based on the input–output data such that the optimal ILC can be executed without any model information. Simulation tests are performed to illustrate the effectiveness and optimality of our proposed ILC method.