Decentralized Optimization of an Interconnected System

A suboptimization procedure of an interconnected system consisting of many subsystems is given. The basic principle of this method is based on the Dantzig and Wolfe's decomposition principle which has been developed to solve the large scale linear programming problem of a special structure with the relatively small scale computer. The optimization is carried out by exchanging the information between the center and the subsystems. If the objective function and the constraint equations are linear convex in the state vector variables of each subsystem, then the procedure is guaranteed to finish in a finite number of iterations. Otherwise, the solutions obtained in each step approach the optimal solutions monotonically. Also shown are minute step by step procedures to be carried out in each iteration by the center and the subsystems together with the rigorous theoretical proof. This method is applicable to the optimization of a wide variety of large scale systems which are composed of many interconnected subsystems such as electrical networks, manufacturing concerns with several plants, communication systems and power systems.