Offline Bayesian Identification of Jump Markov Nonlinear Systems

Abstract

This paper presents a framework for the offline identification of nonlinear switched systems with unknown model structure. Given a set of sampled trajectories, and under the assumption that they were generated by switching among a number of models, we estimate a set of vector fields and a stochastic switching mechanism that best describes the observed data. The switching mechanism is described by a position dependent hidden Markov model that provides the probabilities of the next active model given the current active model and the state vector. The vector fields and the stochastic matrix is obtained by interpolating a set of nodes distributed over a relevant region in the state space. The work follows a Bayesian formulation where the EM-algorithm is used for optimization.