New iterative learning control approaches for nonlinear non-affine MIMO dynamic systems

Abstract

Iterative learning control is a kind of functional approximation approach. In this paper, new types of iterative learning control (ILC) approaches are proposed and analyzed for nonlinear non-affine multi-input-multi-output (MIMO) dynamic systems. First, the important learning performance indices convergence factor (Q-factor) and convergence order (Q-order) are introduced such that the convergence speed of various ILC approaches can be evaluated in a more rigorous and quantitative manner. Second, non-linear ILC: Newton-type ILC approach is proposed to complement the existing linear-type ILC approach in the sense of convergence range and convergence speed. Through rigorous analysis facilitated by the newly introduced performance indices, we show that the Newton-type ILC approach improves the learning convergence significantly in comparison with the linear-type ILC approach, meanwhile requires more of the dynamic system knowledge and are more restrictive on the domain of convergence. Accordingly the Newton-type ILC approach is integrated with the linear-type ILC approach to retain the advantages of both: the linear-type ILC makes the system converge in a much wider range, whereas the Newton-type expedites the convergence when the system is near the equilibrium. It shows that the convergence speed of the Newton-type ILC is faster than that of the linear-type ILC in the sense of Q-factor.