Optimal Synthesis of LTI Koopman Models for Nonlinear Systems with Inputs

A popular technique used to obtain linear representations of nonlinear systems is the so-called Koopman approach, where dynamics are lifted a (possibly infinite dimensional) space through functions called observables. In space, and represented by operator. While theory was originally introduced for autonomous systems, it has been widely derive time-invariant (LTI) models with inputs various approximation schemes such as extended mode decomposition (EDMD). However, recent extensions show that lifting process results in parameter-varying (LPV) model instead an LTI form. As based control successfully practice generally temping use descriptions due simplicity associated tool chain, systematic approach needed synthesise optimal approximations LPV compared ad-hoc EDMD, which on least-squares regression. this work, we introduce exact using ℓ2-gain generalized H2 norm performance measures. We demonstrate advantages proposed modelling procedure EDMD.