Stochastic optimal control for weakly coupled large-scale systems via state and static output feedback

Abstract

In this study, the authors investigate the infinite-horizon linear quadratic control involving state- and control-dependent noise in weakly coupled large-scale systems. In contrast to the existing results, they allow the control and state weighting matrices in the cost function to be indefinite. After establishing an asymptotic structure for the solutions of the stochastic algebraic Riccati equation (SARE), a weak coupling parameter-independent control is provided. Moreover, by solving the reduced-order linear matrix inequality (LMI), they can easily obtain the proposed control without using any numerical algorithms. As a result, although the small positive weak coupling parameter that connects the other subsystems is very small or unknown, it is possible to compute the desired controller. Finally, the extension of the result of the study to the static output feedback control problem is discussed by considering the Lagrange multiplier method.