Nonlinear Dynamical System Learning with Guaranteed Topological Property of Trajectories

Abstract

Dynamical system learning, also known as system identification, is a powerful tool for modeling unknown systems from data. However, guaranteeing properties such as stability of the obtained model is generally difficult, especially for complex nonlinear models. Therefore, for industrial applications, a reliable learning method that can ensure that the model has some desirable properties is required. In this paper, a novel method for learning a nonlinear model with guaranteed topological properties is proposed. The method employs a model structure represented by transforming the internal state, defined by an internal model with simple known dynamic properties, by a homeomorphic map. This enables to learn a model that guarantees not only the stability of the model but also the existence of limit cycles and other topological properties of the state trajectories in state space.