Numerical Computation of Linear Quadratic Control Problem for Singularly Perturbed Stochastic Systems

In this paper, linear quadratic control with state-dependent noise for singularly perturbed stochastic systems (SPSS) is addressed. After establishing the asymptotic structure of the stochastic algebraic Riccati equation (SARE), a new iterative algorithm that combine the 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 both attained. As another important feature, a high-order state feedback controller by means of the obtained iterative solution is given and the degradation of the cost performance is investigated for the stochastic case for the first time. Finally, in order to demonstrate the efficiency of the proposed algorithm, numerical example is given for practical megawatt-frequency control problem.