Multicriteria control problems for stochastic sequences

The present article is devoted to the multicriteria problem of the optimal control for stochastic sequences with the infinite horizon. The general method of attack is based on the method of constraints. The main theoretical result is formulated as the Kuhn-Tucker theorem which gives the necessary and sufficient conditions of the optimality; besides, the description of the class of strategies is presented which is sufficient for solving the problem. The last section is devoted to the investigation of the linear system with the quadratic and linear criteria.