System structure rendering iterative learning convergent

Abstract

This paper attempts to give a mathematical and physical interpretation of practice-based learning (so-called "iterative learning control") from the viewpoint of input-output "passivity" of system dynamics. It is shown from an axiomatic argument that the passivity and dissipativity of a pair of input and output for a class of linear dynamical systems with positive real or strictly positive real transfer matrices play a crucial role in the ability of learning. This observation is extended to a class of nonlinear robot dynamics which naturally satisfy passivity and dissipativity. Ability of learning for a class of robotic tasks such as a tool-endpoint is in contact with an object and a soft fingertip presses a rigid object (i.e., impedance control) is also analyzed in detail. Finally relations between dissipativity and system invertibility are discussed.