System concepts in Kron's polyhedron model and the scattering problem

Abstract

Abstract Kron's polyhedron model based on a sequence of transformations related to the orthogonal electrical network problem was proposed for a wide range of system problems. The scattering formulation for a flow process introduces a similar sequence of ‘ obstacles ’ and can form an analytical basis for many of the concepts discussed by Kron. It can be associated with the system problems incorporating an optimality condition and the updating of a priori information, and can also be identified in the sweep method of solution of the two-point boundary-value problems for optimal control and estimation, which would appear to be related to the concept of wave propagation in Kron's model. The sequential networks in the polyhedron model and the scattering problem thus provide a basic analytical structure which has important applications in general systems theory.