Linear Quadratic Optimal Control of Stochastic Discrete-Time Systems with λ-Policy Iteration

In this paper, an algorithm of λ-policy iteration is proposed to solve the linear quadratic regulator (LQR) problem for stochastic discrete-time systems. Firstly, an algebra Riccati equation (ARE) of the stochastic discrete-time systems is established. Then, the offline policy iteration (PI) and the offline value iteration (VI) are developed to solve the ARE. Based on the PI and the VI, the λ-policy iteration is applied to the LQR problem of stochastic discrete-time systems. In contrast to the PI, the initial stabilizing control policy is not required. Besides, the convergence speed is faster than the VI. Meanwhile, the convergence of the proposed λ-policy iteration is discussed. Finally, a simulation example is given to verify the effectiveness of the λ-policy iteration.