Newton Method Based ILC

Summary

This chapter covers the Newton method that lends itself to iterative learning control (ILC) design in an algebraic setting and permits a direct extension of the lifting approach from linear to nonlinear dynamics. The Newton method is a longstanding technique in numerical analysis. As the chapter demonstrates, it is possible to formulate some nonlinear ILC design problems as a Newton iteration and used well‐established results from this area of numerical analysis to develop efficient and reliable solutions. The Newton ILC law is a special case of the Newton method and, hence, it inherits the convergence properties of this method. The need for constrained ILC design is motivated by application areas. The chapter provides a Newton ILC design in the presence of input constraints, based on a penalty function and an iterative method for solving an unconstrained nonlinear optimization problem.