Iterative learning control of non-identical desired trajectories for a class of nonlinear time-varying systems

A new iterative learning control algorithm was proposed for a class of unknown nonlinear time-varying systems with exogenous disturbance, and the algorithm is applied to the case of variable desired trajectories between any two consecutive iterations. Firstly, the inverse control with unknown parameters is designed; and then a wavelet series are employed to approximate the inverse plant nonlinearities, whose ideal coefficients are irrelevant to the desired trajectories; finally, the wavelet approximation coefficients are adapted by iteratively learning, and the robust iterative learning control law is synthesized based on the variable structure technique to overcome the system uncertainty. The algorithm convergence analysis showed that the differences between actual and ideal coefficients are monotonically decreasing with the iteration. The convergence of the tracking error was shown by a simulation on a manipulator, which demonstrated the effectiveness of the algorithm.