Finite-horizon dynamic compensation of Markov Jump Linear Systems without mode observation

In this paper, we address finite-horizon optimal control of Markov Jump Linear Systems with non-observed discrete-valued system state via dynamic output feedback. It has been shown that the optimal control law for this problem is intractable. For this reason, we assume a mode-independent control policy consisting of a linear time-variant estimator that reconstructs the continuous-valued state from noisy measurements, and a linear time-variant regulator that maps the state estimate to control inputs. To the best of our knowledge, this problem remained unsolved because even under the assumption of a linear control law, the separation between the estimator and the regulator does not hold. However, by minimizing an upper bound on the true costs induced by the control, we are able to design an iterative algorithm for computation of the controller parameters whose convergence is shown. The proposed algorithm is demonstrated by means of a simulation.