Formulas for Discrete Time LQR, LQG, LEQG and Minimax LQG Optimal Control Problems

Abstract The purpose of this paper is to provide a unified presentation of the formulas arising in the discrete-time finite-horizon linear Linear Quadratic Regulator problem, the Linear Quadratic Gaussian problem, the Linear Exponential of Quadratic Gaussian problem, and the minimax Linear Quadratic Gaussian problem. For these classes of optimal control problems, the paper presents formulas for optimal policies and optimal cost. This allows for a comparison between these different optimal control problems.