Decentralized multicriteria optimization of linear stochastic systems

By adopting a decision-theoretic approach and under the noncooperative equilibrium solution concept of game theory, decentralized multicriteria optimization of stochastic linear systems with quasiclassical information patterns is discussed. First, the static -person quadratic decision problem is considered, and sufficiency conditions are derived for existence of a unique equilibrium solution when the primitive random variables have a priori known but arbitrary probability distributions with finite second-order moments. The optimal strategies are given in the form of the limit of a convergent sequence which is shown to admit a closed-form linear solution for the special case of Gaussian distributions. Then, this result is generalized to dynamic LQG problems, and a general theorem is proven, which states that under the one-step-delay observation sharing pattern this class of systems admit unique affine equilibrium solutions. This result, however, no longer holds true under the one-step-delay sharing pattern, and additional criteria have to be introduced in this case. These results are then interpreted within the context of LQG team problems, so as to generalize and unify some of the results found in the literature on team problems.