Connection between stochastic control of Markov process parameter and transportation problem

Consider a functioning of discrete Markov process in random environment. That is the process behavior is defined by some randomly varying parameter. Suppose that stationary distributions of the process under fixed meanings of the parameter are known. A problem is to choose a control of parameter ramdom variation so that the stationary distribution of obtained process equals to probability mixture of stationary distributions of this process under fixed parameter meanings. An algorytm which put a mutually synonymous accordance between a set of all stochastic controls and a set of all accessible solutions of some transportation problem and an interior of some multidimensional cube is constructed.