Optimal control with a finite Markov chain and a fuzzy given probability measure

Karmanov A., Popadko V.

The article poses the problem of controlling a homogeneous Markov chain, which is often found in applications, under conditions when the probability measure on the trajectory space of this chain is not clearly defined, i.e. the measure is an unknown element of some certain set of probability measures. In this case, the problem of optimal control with such Markov chain with a guaranteed income functional and maximum guaranteed income optimality criterion is formulated. An iterative procedure for solving the problem is given.

Keywords:homogeneous finite Markov chain with income controlled finite Markov chain, Cesiaro limit of the stochastic matrix, the Markov chain optimal control with income.