Coordination and Sensitivity Analysis of a Large Scale System with Performance Interaction

Abstract

A large scale system structure is considered for the case where the performance functional is not a simple sum of local performance indices. A decomposition method of the large scale problem consists of modifying the local performance functionals according to the global performance requirements.The large scale problem and its decomposition are formulated in Hilbert space; a formulation as a control problem is also presented as an example of possible detailed formulations. The properties of the decomposed problem are investigated. A new method of coordination based on an alternative approach to the variable operator method in Hilbert space is described; the basic properties of the method are analysed. A special feature of the variable operator method is stressed, which makes it possible to apply the method to large scale problems.The variable operator method is also useful in evaluating the sensitivity of the large scale structure to the coordination variables. A general discussion of sensitivity properties of large scale systems is also included. The large scale system structure and the method of evaluating its sensitivity can be of particular interest when applied to environmental control.