Iterative Robust Experiment Design for MIMO System Identification via the S-Lemma

Optimal input design plays an important role in system identification for complex and multivariable systems. A known paradox in input design is that the optimal inputs depend on the true but unknown system. The aim of this paper is to design inputs for multivariable systems that are robust to all system variations within a given continuous uncertainty set. In the presented approach, the robust design problem is cast as an infinite-dimensional min-max optimization problem, and tackled via the S-lemma in an iterative approximation scheme. Experimental results from a multivariable motion system show that the algorithm enables significant robustness improvements.