Robust Iterative Learning Control for linear systems with time-varying parametric uncertainties

In this paper, we present a robust Iterative Learning Control (ILC) design for linear systems in the presence of time-varying parametric uncertainties. The robust ILC design is formulated as a min-max problem using a quadratic performance criterion subject to constraints of the control input update where the system model contains time-varying parametric uncertainties. An upper bound of the worst-case performance is employed in the min-max problem. Subsequently, applying Lagrangian duality to the min-max problem, we derive a dual problem which is reformulated as a convex optimization over linear matrix inequalities (LMIs). As a result, iterative input updates can be obtained by solving a series of LMI problems. We give an LMI algorithm for the robust ILC design and prove the convergence of the control input and the error. Finally, a numerical example is presented to illustrate the effectiveness of the proposed algorithm.