Optimization-Based Constrained Iterative Learning Control

We consider the problem of synthesis of iterative learning control (ILC) schemes for constrained linear systems executing a repetitive task. The ILC problem with affine constraints and quadratic objective functions is formulated as a convex quadratic program, for which there exist computationally efficient solvers. The key difference between standard convex optimization and the corresponding constrained ILC problem is that each iteration in the latter requires an experiment run. We implement an interior-point-type method to reduce the number of iterations (and hence the number of experiment runs). We discuss the system-theoretic interpretations of the resulting optimization problem that lead to reductions in computational complexity and compare the performance of the implementation based on the interior-point method to another approach based on the active set method on a simulation example. We demonstrate the technique on a prototype wafer stage system with actuator saturation constraints and ℓ_2 norm of the tracking error as the objective function. The key contribution of this paper is the systematic use of numerical tools from constrained convex optimization in the ILC design.