Convergence theory for multi‐input discrete‐time iterative learning control with Coulomb friction, continuous outputs, and input bounds

Abstract

We consider the problem of discrete-time iterative learning control (ILC) for position trajectory tracking of multiple-input, multiple-output systems with Coulomb friction, bounds on the inputs, and equal static and sliding coefficients of friction. Only position measurements are assumed available. No velocity measurements are assumed available. We present an ILC controller and a proof of convergence to zero tracking error, provided the associated learning gain matrices are scalar-scaled with a sufficiently small positive scalar. We also show that non-diagonal learning gain matrices satisfying the same prescribed conditions do not lead to the same convergence property. To the best of our knowledge, for problems with Coulomb friction, this paper represents a first convergence theory for the discrete-time ILC problem with multiple-inputs and multiple-bounded-outputs; previous work presented the theory only for the single-input, single-output problem.