Learning globally linear predictors using deep Koopman embeddings with application to marine vehicles

Abstract

Linearity of the model for controlled dynamical systems is a very desirable property because of its simplicity in the state prediction and control. Koopman operator theory provides a framework for global mapping of a nonlinear system into an equivalent linear system. The goal of this work is to exploit Koopman theory and modern machine learning techniques to find the linear system representation of the underlying nonlinear system for future state predictions. The model generated in this way is completely data driven and requires no a priori knowledge of the underlying dynamics system. The model is applied to two marine vehicles whose trajectories are generated using simulation and evaluated against common model identification techniques. The results show that proposed method is comparable to conventional identification methods and even outperforms them in cases when complex nonlinear dynamics, which is often neglected, becomes relevant.