Generalization of norm optimal ILC for nonlinear systems with constraints

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