Data-Driven Koopman Controller Synthesis Based on the Extended ${\mathcal{H}}_2$ Norm Characterization

Abstract

This paper presents a new data-driven controller synthesis based on the Koopman operator and the extended ${\mathcal{H}}_2$ norm characterization of discrete-time linear systems. We model dynamical systems as polytope sets which are derived from multiple data-driven linear models obtained by the finite approximation of the Koopman operator and then used to design robust feedback controllers combined with the ${\mathcal{H}}_2$ norm characterization. The use of the ${\mathcal{H}}_2$ norm characterization is aimed to deal with the model uncertainty that arises due to the nature of the data-driven setting of the problem. The effectiveness of the proposed controller synthesis is investigated through numerical simulations.

6 pages, 6 figures

References in corpus (1)

• Extended dynamic mode decomposition with dictionary learning: a data-driven adaptive spectral decomposition of the Koopman operator