High-order approximation of stochastic linear quadratic control for weakly-coupled large-scale systems

Abstract

In this paper, stochastic linear quadratic (LQ) control with state-dependent noise for weakly coupled largescale systems is discussed. After establishing the asymptotic structure of the stochastic algebraic Riccati equation (SARE), an iterative algorithm that Newton's method combined with another fixed point algorithm is derived for the first time. As a result, the quadratic convergence and the reduced-order computation in the same dimension of the subsystems are both attained. As another important features, the high-order approximate controller that is based on the iterative solutions is proposed. Using such controller, the degradation of the cost is investigated. Moreover, as an important extension, the stochastic LQ control with state- and control-dependent noise for weakly coupled large-scale systems is also addressed as the aspect of the numerical scheme. Numerical example demonstrates the behavior of the resulting hybrid algorithm.