Decentralized Control Design for Interconnected Systems Based on A Centralized Reference Controller

This paper deals with the decentralized control of interconnected systems, where each subsystem has models of all other subsystems (subject to uncertainty). A decentralized controller is constructed based on a reference centralized controller. It is shown that when a priori knowledge of each subsystem about the other subsystems' models is exact, then the decentralized closed-loop system can perform exactly the same as its centralized counterpart. An easy-to-check necessary and sufficient condition for the internal stability of the decentralized closed-loop system is obtained. Moreover, the stability of the closed-loop system in presence of the perturbation in the parameters of the system is investigated, and it is shown that the decentralized control system is likely more robust than its centralized counterpart. A proper cost function is then defined to measure the closeness of the decentralized closed-loop system to its centralized counterpart. This enables the designer to obtain the maximum allowable standard deviation for the modeling errors of the subsystems to achieve a satisfactorily small performance deviation with a sufficiently high probability. The effectiveness of the proposed method is demonstrated in one numerical example