Perfect tracking for maximum-phase nonlinear systems by iterative learning control

A method to track a desired trajectory by iterative learning control is proposed for uncertain maximum-phase nonlinear systems. The relation between the variations in the initial state, input and output is derived and it is shown that the inverse mapping from the desired output to the initial state and input is stable using the time reversal of unstable manifolds for a maximum-phase system as given by Doyle et al. Based on these facts, an input update law is proposed to find the initial state and the input for perfect tracking. Also, it is shown that perfect tracking can be made possible over a finite control horizon by using a non-causal input starting at any fixed state. Simulation results show that the proposed method works well.

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