Control of Partially Observed Discrete-Time Jump Systems

The problem of control of discrete-time linear Gaussian systems with Markovian jump parameters is considered in this paper, where both the system state and jump (system mode) can not be observed perfectly. The Dynamic Programming equation is expressed in terms of optimal mode-conditioned cost-to-go and a quadratic control-independent parametrization is used to find a closed form solution for the approximate control. The resulting control is a linear function in the mode-conditioned state estimate and nonlinear in the mode estimate. The control gains are governed by a set of coupled Riccati difference equations. Simulation examples are provided to show the performance of the proposed suboptimal, but easily implementable, control scheme where the state and mode estimates can be obtained through the Interacting Multiple Model estimation algorithm.