Optimal tracking control for stochastic discrete-time systems based on improved Riccati iterative algorithm

In this paper, an improved stochastic algebraic Riccati (SAR) iterative algorithm based on numerical iterative is adopted to solve the stochastic linear quadratic optimal tracking (SLQT) control problem for stochastic discrete-time systems. Firstly, an augmented system composed of the stochastic discrete-time system and command generator is constructed. Then, the augmented stochastic algebraic Riccati equation (SARE) is derived based on the augmented system and the corresponding SAR iterative algorithm is obtained according to the idea of value iteration (VI) algorithm. Secondly, an improved SAR iterative algorithm is raised based on the given SAR iterative algorithm and combined with the numerical iterative method. Finally, simulation results verify the effectiveness of the proposed algorithm.