An Implicit Iterative Algorithm for Linear Quadratic Optimal Control Problem

This paper investigates linear quadratic regulator(LQR) problem of linear stochastic systems. An novel algorithm is proposed to solve the general algebraic Riccati equation(GARE) derived from linear stochastic systems based on successive over-relaxation technique. With some initial conditions satisfied, the monotone convergence can be guaranteed, and an initial value selection method is proposed. Furthermore, a numerical example is given to demonstrate the effectiveness of the algorithm.