Towards a sub-optimal solution of a partially observed state dependent JLQ problem

In this paper, we introduce a class of jump linear systems whose regime indicators are deterministic functions of the states of the system but the parameters of both the function and the system are uncertain. We assume that only their pdf´s which are uniform are available. Furthermore, only part of the system states are observed for feedback control. The problem is to find an admissible control which optimizes the expected value of a quadratic loss function. We show that by augmenting the system with an observer and defining an estimated regime indicator, this class of problem can be reformulated to become a jump linear system whose regime transition rates are state and control dependent and fits nicely into the framework due to Sworder and Robinson (1973). By letting the speed measure equals to the estimated regime indicator, we simplified the governing equations of the optimal control. As a result, a sub-optimal but simple solution of the partially observed JLQ problem can be found