Pair-wise decomposition and coordinated control of complex systems

Pair-wise decomposition and coordinated control for complex interconnected systems with any information structure constraints are proposed in this paper. Based on the inclusion principle, a permuted inclusion principle is presented to expand the system into an expanded space, from which a recurrent reverse order of pair-wise subsystems is extracted. By a standard LQ control, pair-wise controllers can be designed to stabilize and coordinate the pair-wise subsystems. According to these controllers, a coordinated compensator of subsystem interconnections is introduced in order to obtain a coordination-based controller for the expanded system. Therefore, a coordinated controller of the system can be contracted from the expanded space under the conditions of the inclusion principle. Moreover, a sufficient condition of connective stability for the system is also proved by the Lyapunov function and M-matrix. A main advantage of the proposed decomposition and control is that it allows any variation of information structure constraints of the system, especially the increase and decrease of subsystem numbers. Finally, the effectiveness of the proposed methodology is demonstrated by an application of automatic generation control to a four-area electric power system.