Newton method based iterative learning control for discrete non-linear systems

Abstract

Significant progress has been achieved in terms of both theory and industrial applications of iterative learning control (ILC) in the past decade. However, the techniques of solving non-linear ILC problems are still under development. The main result of this paper is a novel non-linear ILC algorithm that utilizes the capability of the Newton method. By setting up links between non-linear ILC problems and non-linear multivariable equations, the Newton method is introduced into the ILC framework. The implementation of the new algorithm allows one to decompose a nonlinear ILC problem into a sequence of linear time-varying ILC problems. Simulations on a discrete non-linear system and a manipulator model display its advantages. Conditions for its semi-local convergence are analysed. Links of ILC with existing non-linear topics are pointed out as ways to construct new non-linear ILC schemes. Potential improvements are discussed for future work.