Linearly Constrained LQ and LQG Optimal Control

Abstract It has recently been shown that the logarithmic barrier method for solving finite-dimensional, linearly constrained quadratic optimization problems can be extended to an infinite-dimensional setting with complexity estimates similar to the finite dimensional case. As a consequence, an efficient computational method for solving the linearly constrained LQ control problem is now available. In this paper, we solve the linearly constrained LQG control problem by generalizing the Separation Theorem. We show how the logarithmic barrier method can be used to determine the optimal control for the constrained LQG problem.