ON THE ROBUST OPTIMAL DESIGN AND CONVERGENCE SPEED ANALYSIS OF ITERATIVE LEARNING CONTROL APPROACHES

摘要

In Iterative Learning Control design, convergence speed along the iteration domain is one of the most important performance factors. In this paper, we aim at achieving fastest convergence speed (time-optimal) for a variety of nonlinear non-affine Single-Input-Single-Output (SISO) plants, and focus on the family of the linear type iterative learning controllers, including first-order ILC and higher-order ILC. The control objective can be formulated as a kind of robust optimization: optimizing the worst case performance in the presence of the interval uncertainties. To quantify convergence speed, a learning performance index ― Q-factor ― is employed. The optimal learning gain is then obtained by solving a Min-max problem. From the robust optimal design, we also reach the following conclusion: under the same interval uncertainty and applying the same min-max design which is robust and optimal, the Q-factor of ILC sequences of lower order ILC is always less than that of higher order ILC in terms of time-weighted norm. In the sequel, the first order ILC achieves the fastest convergence speed in the iteration domain.