A Method for Identification of Markovian Jump ARX Processes

In this paper, we address the problem of identification of Markovian jump ARX systems in the case where there is no a priori knowledge on the statistics of the process noise. The only assumptions made are the availability of known upper bounds on the subsystems order and noise level. The proposed method leverages available results to identify the subsystems models and provides a novel way to estimate the transition probability matrix of the switching in the presence of uncertainty. More precisely, since one cannot observe the exact switching sequence, the problem of estimating the transition probability matrix is formulated as a robust optimization problem, where one maximizes the minimum of the probability of all possible switching sequences. We show that this robust optimization problem can be efficiently solved by providing an equivalent convex formulation that can be solved using off-the-shelf software. Several academic examples are provided which illustrate the effectiveness of proposed approach.