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

TL;DR

This paper introduces a novel data-driven control synthesis method leveraging the Koopman operator and extended $$ norm to design robust controllers for uncertain discrete-time systems, validated through simulations.

Contribution

It proposes a new data-driven controller synthesis approach combining Koopman operator theory with extended $$ norm for robust control design.

Findings

Effective in handling model uncertainty

Demonstrated robustness through numerical simulations

Provides a systematic data-driven control framework

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.