On optimality and certainty equivalence in output feedback control of constrained uncertain linear systems

We address the problem of finite-horizon optimal control of uncertain discrete-time SISO linear systems with input constraints. The uncertainty for the problem analyzed is related to incomplete state information (output feedback) and stochastic disturbances. We analyze the optimal solutions for short optimization horizons when the disturbances and the initial state are Gaussian random vectors. We also consider two suboptimal strategies, one of which is known as Certainty Equivalent Control.