Generalization of norm optimal ILC for nonlinear systems with constraints

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• Norm optimal ILC for LTI systems is extended to constrained nonlinear systems.
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• The nominal model is explicitly corrected based on past trial data as a first step.
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• The structure of the model correction can be defined arbitrarily.
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• The optimal next trial input signal is calculated in a second step.
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• Both steps are solved efficiently using a sparse interior point method.

This paper discusses a generalization of norm optimal iterative learning control (ilc) for nonlinear systems with constraints. The conventional norm optimal ilc for linear time invariant systems formulates an update equation as a closed form solution of the minimization of a quadratic cost function. In this cost function the next trial's tracking error is approximated by implicitly adding a correction to the model. The proposed approach makes two adaptations to the conventional approach: the model correction is explicitly estimated, and the cost function is minimized using a direct optimal control approach resulting in nonlinear programming problems. An efficient solution strategy for such problems is developed, using a sparse implementation of an interior point method, such that long data records can be efficiently processed. The proposed approach is validated experimentally.