Abstract
This chapter deals with Iterative Learning Control ILC schemes to solve the trajectory tracking problem of affine and non-affine nonlinear systems performing repetitive tasks. Two ILC laws are presented; the first law is a simple on-line 2D-type learning control for affine nonlinear systems. In addition, an initial condition algorithm is generated to provide the initial state value at each iteration automatically. To prove the asymptotic stability of the closed loop system over the whole finite time interval when the iteration number tends to infinity, \(\lambda \)-norm is used, as the topological measure. The second law is the on-line P-type ILC applied to non affine nonlinear systems. The asymptotic stability of the closed loop system is guaranteed upon the use of a Lyapunov-like positive definite sequence, which is shown to be monotonically decreasing under the proposed control scheme. Finally, simulation results on nonlinear system are provided to illustrate the effectiveness of the two controllers.
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