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Stochastic control design chooses the controller that makes the closed-loop behavior as close as possible to the desired one. The fully probabilistic design describes both the closed-loop and its desired behavior in probabilistic terms and uses the Kullback-Leibler divergence as their proximity measure. Such a design provides explicit minimizer, which opens a way for a simpler approximations of analytically infeasible cases. The current formulations are oriented towards finite-horizon design. Consequently, the optimal strategy is nonstationary one. This paper provides infinite-horizon problem formulation and solution. It leads to a stationary strategy whose approximation is much easier.

STATIONARY FULLY PROBABILISTIC CONTROL DESIGN