Accession Number : AD0611804

Title :   SOME NETWORK INTERPRETATIONS OF SYSTEM PROBLEMS,

Corporate Author : COLUMBIA UNIV NEW YORK SCHOOL OF ENGINEERING AND APPLIED SCIENCE

Personal Author(s) : Stern,Thomas E.

Report Date : DEC 1964

Pagination or Media Count : 86

Abstract : Certain special properties are set forth of networks which can be exploited in synthesizing network analogs for two basic types of extremum problems. On the one hand, the fact that the equilibria of resistive reciprocal networks can be identified with stationary points of their associated dissipation functions leads in a natural way to the construction of network analogs for mathematical programming problems. On the other hand, the fact that Lagrangian networks behave in such a manner as to make a certain functional stationary leads to the formulation of networks which generate extremals for variational problems. It should be emphasized that these analogs are meant simply as network interpretations of extremum problems. The actual use to which they are put must depend upon the inclination of the individual, and on the particular problem being analyzed. Among their possible uses are, 1) as a heuristic tool to promote a better 'physical' understanding of a problem, 2) as a means of suggesting more efficient computational schemes for solving extremum problems, and 3) as a direct analog to be used either alone or in conjunction with other devices for the solution of an extremum problem. (Author)

Descriptors :   (*ELECTRICAL NETWORKS, MATHEMATICAL PROGRAMMING), (*OPTIMIZATION, CONTROL SYSTEMS), (*CALCULUS OF VARIATIONS, ELECTRICAL NETWORKS), STABILITY, FUNCTIONAL ANALYSIS, PARTIAL DIFFERENTIAL EQUATIONS, NUMERICAL ANALYSIS

Distribution Statement : APPROVED FOR PUBLIC RELEASE