Zero-Order Optimization-Based Iterative Learning Control

We consider an optimization-based iterative learning control (ILC) approach for nonlinear systems where the control input is obtained as the solution of a constrained nonlinear program (NLP). The NLP formulation is based on a - possibly nonlinear - nominal model corrected by the output error which has been observed in the previous trial. Assuming that the sensitivities of the nominal model are sufficiently close to the sensitivities of the real system, we show local convergence of the proposed ILC method to a generally suboptimal solution and derive a bound on the loss of optimality. Even though the algorithm does not require any exact sensitivity information of the true process, it can recover the optimal control input in two special cases: Assuming that the sensitivities are sufficiently similar, the optimal solution is obtained (1) if it lies at a vertex of the feasible set, i.e. it is fully determined by the constraints, or (2) if a reference tracking problem is considered and optimal tracking is feasible.