Near-Optimal Recursive Identification for Markov Switched Systems

This paper tackles the problem of identifying the parameters of a class of stochastic switched systems, where the active subsystem is determined by a Markov chain. This class includes autoregressive models with exogenous inputs (ARX) for which the parameters switch according to a Markov chain and general Markov Jump Linear Systems (MJLSs) with full-state information. The transition probabilities of the Markov chain are assumed to be known, but the active subsystem is unknown. A recursive identification method for the joint maximum a posteriori probability estimate of these parameters and of the unknown mode is proposed relying on relaxed dynamic programming. The method is guaranteed to provide an estimate whose joint posteriori probability is within a constant factor of that of the optimal estimate while reducing the computational complexity. The method is illustrated through a numerical example.