Optimization Based Weighting Matrices Design for Norm Optimal Iterative Learning Control

This paper focuses on Norm-Optimal Iterative Learning Control (NO-ILC) framework for Single-Input-Single-Output (SISO) Linear Time Invariant (LTI) systems and considers the weighting matrices design problem. The ideal design of weighting matrices should ensure Robust Monotonic Convergence (RMC) against modeling uncertainties while maximizing the convergence speed and minimizing the steady state error. The state-of-art RMC design methodologies either lead to conservative performance or require manual tunings. This paper provides a methodology to systematically achieve an optimal balance between robustness, convergence speed and steady state error. To this end, optimization problems are formulated at each frequency to maximize the convergence speed and minimize the steady state error. Two optimization formulations are proposed: one for an optimal nominal performance and one for an optimal performance against uncertainties. Both formulations offer a systematic approach for designing the weighting matrices for NO-ILC, thereby eliminating the manual tuning process and avoiding an unnecessarily conservative design. A simulation example is given to confirm the analysis and demonstrate the utility of the developed methodologies to design the weighting matrices.