Practical implementation of the solution of the stabilization problem for a linear system with discontinuous random drift by indirect observations

We study the implementation of the optimal control strategy obtained in [1] and supplemented in [2]. The algorithm for optimal stabilization of a linear stochastic differential system in a position determined by a piecewise constant Markov drift has been tested in a substantial number of model experiments. The drift value is observed indirectly; i.e., the control problem is solved in the statement with incomplete information. Practical implementation is complicated by the instability of Euler–Maruyama numerical schemes that implement the Wonham filter, which is a key element of the optimal control strategy. To perform calculations, the Wonham filter is approximated by stable schemes based on the optimal filtering of Markov chains by discretized observations [3]. These schemes have different implementation complexity and orders of accuracy. The paper presents a comparative analysis of the control performance for various stable approximations to the Wonham filter and its typical implementation using the Euler–Maruyama scheme. In addition, three versions of discretized filters are compared and final recommendations are given for their application in the problem of stabilizing a system with hopping drift.