November 28, 2024, 15:30, SP2 416-2

TITLE: Linear control theory for nonlinear systems via Koopman lifting

ABSTRACT: The idea of analyzing nonlinear control systems via techniques developed for the linear case by lifting the dynamics to an infinite-dimensional space is well known and already dates back to the works by Koopman and Carleman in the 1930s. More recently, there has been renewed interest into Koopman-based control systems, mainly due to progress that has been mode from a numerical perspective, e.g., the (extended) dynamic mode decomposition. This talk discusses the use of Koopman-lifted systems in the context of optimal/minimal (feedback) control problems. In particular, it will be shown that certain energy functionals, typically described by a nonlinear Hamilton-Jacobi-Bellman equation, can be linked to a nonlinear operator equation which shares similarities to the Lyapunov equation. Theoretical approximation results for this equation will be discussed and subsequently be utilized for system theoretic model reduction techniques such as balanced truncation.