Near-Optimal Control for Singularly Perturbed Stochastic Systems

Abstract

This paper addresses linear quadratic control with state-dependent noise for singularly perturbed stochastic systems (SPSS). First, the asymptotic structure of the stochastic algebraic Riccati equation (SARE) is established for two cases. Second, a new iterative algorithm that combines Newton's method with the fixed point algorithm is established. As a result, the quadratic convergence and the reduced-order computation in the same dimension of the subsystem are attained. As another important feature, a high-order state feedback controller that uses the obtained iterative solution is given and the degradation of the cost performance is investigated for the stochastic case for the first time. Furthermore, the parameter independent controller is also given in case the singular perturbation is unknown. Finally, in order to demonstrate the efficiency of the proposed algorithm, a numerical example is given for the practical megawatt-frequency control problem.