Iterative Learning Control for Nonlinear Systems Based on New Updated Newton Methods

A new iterative learning algorithm for nonlinear systems based on updated Newton method is investigated. The exchange row updated method is employed to derive the approximation of derivatives of the output function. The inverse of approximation of derivatives of the output function can be obtained by simple recurrent formula. This new algorithm has advantage of simplified calculation of the iterative learning control law in every iterative learning process. Sufficient conditions for convergence of this new updated Newton algorithm are given and proved. Moreover, a Secant-type iteratvie learning control of new updated Newton mehtod is presented. This approach avoid calculating partial derivatives such that the calculate work is largely reduced.