Optimal linear mean square filter for the operation mode of continuous‐time Markovian jump linear systems

Abstract

This paper makes a further foray on the study of the filtering problem for the class of Markov jump linear systems (MJLSs). The authors shall be particularly interested in the filtering problem for the Markov jump parameter (the operation mode). Previous result in the literature on this problem has been obtained by Wonham, which has derived an optimal non-linear filter for this problem. The main hindrance with Wonham's result, in the context of the optimal control problem for MJLS with partial observation of the operation mode, is that it introduces a great deal of non-linearity in the Hamilton-Jacobi-Belman equation, which makes it difficult to get an explicit closed solution for the control problem. Motivated, in part, by this, the main contribution of this paper is to devise an optimal linear filter for the mode operation, which they believe could be more favourable in the solution of the control problem with partial observations. In addition, relying on Murayama's stochastic numerical method and the results by Chenggui-Yuan, they carry out simulation of Wonham's filter, and the one devised in this paper, in order to compare their performances.