A Feasible Method in the Decentralized Optimization of Large Scale Dynamical Systems

Abstract

A method is described for obtaining “feasible solutions” in the decentralized optimization of large scale dynamical systems. The “feasible solution” here means the solution which always satisfies the output-input relations among all the interconnected subsystems.
In the method proposed here, the paths of output variables of subsystems are first assumed, the optimization of each subsystem is carried out taking into account the output-input relations as equality constraints and then the condition for the optimal control of the entire system is checked to see whether or not the assumed values of the output variables should be corrected. Therefore, in contrast with the usual decentralized optimal control, the feasible solutions which are realizable in real systems will be obtained after each cycle of the iterative computation of the optimal control path.
The existence theorem of the optimal paths of output variables which make the condition for the optimal control of the subsystems identical with those of the entire system is proved.
An iterative procedure in a function space to find the optimal paths of output variables is proposed and then the stable convergence of the variables into the optimal paths is assured through Lyapunov stability criteria.
A simple example is dealt with to illustrate how the proposed method works.