Descriptor-variable approach to modeling and optimization of large-scale systems. Final report, March 1976--February 1979

Abstract

A new approach to modeling and analysis of systems is presented that exploits the underlying structure of the system. The development of the approach focuses on a new modeling form, called 'descriptor variable' systems, that was first introduced in this research. Key concepts concerning the classification and solution of descriptor-variable systems are identified, and theories are presented for the linear case, the time-invariant linear case, and the nonlinear case. Several standard systems notions are demonstrated to have interesting interpretations when analyzed via descriptor-variable theory. The approach developed also focuses on the optimization of large-scale systems. Descriptor variable models are convenient representations of subsystems in an interconnected network, and optimization of these models via dynamic programming is described. A general procedure for the optimization of large-scale systems, called spatial dynamic programming, is presented where the optimization is spatially decomposed in the way standard dynamic programming temporally decomposes the optimization of dynamical systems. Applications of this approach to large-scale economic markets and power systems are discussed.