Fully probabilistic control design for Markov chains

Control design for stochastic systems is usually based on the optimization of the expected value of a suitably chosen loss function. This approach, although simple, can lead to computational problems. Therefore, it is worth searching alternative formulation of this problem which leads to more tractable design. In this paper we present an alternative that leads to simpler form of design equations. The proposed controller minimizes the Kullback-Leibler distance between the actual and the ideal probabilistic description of the closed loop behaviors. This theory is also applied to Markov chains and promising results are obtained.