Judicaël Mohet (UNamur)

In this work, we present a novel approach for the observer design of nonlinear systems based on a Koopman operator framework. The (linear) dual Koopman system, associated with a nonlinear dynamic, is introduced and analyzed in an infinite dimensional context. Moreover, new concepts of observability and detectability are defined in the dual Koopman system, which are shown to be equivalent to the observability and detectability of the nonlinear system, respectively. The theoretical framework is applied to a class of holomorphic dynamics. For this class, a Luenberger-type observer is designed for the dual Koopman system via a spectral method, yielding an estimate of the state of the nonlinear system. Spectral observability and detectability conditions are derived in this setting, and the exponential convergence of the Koopman observer is shown 

Authors: Judicaël Mohet, Alexandre Mauroy and Joseph Winkin