On certainty equivalence of stochastic optimal control problem

This paper is concerned with the optimal control of discrete-time stochastic linear systems with respect to a quadratic performance criterion. It is assumed that the system is subject to additive system noise and that the state variables arc measured with additive measurement noise. It is shown that certainty equivalence, previously proven for the so-called Linear-Quadralic-Gaussian problem, holds even if the system noise, the measurement noise and/or the initial state of the system arc non-gaussian. mutually and time-wise dependent.