
Accession Number : AD0702519
Title : OPTIMUM CONTROL OF DISTRIBUTED PARAMETER SYSTEMS WITH TWO INDEPENDENT VARIABLES.
Descriptive Note : Final rept.,
Corporate Author : AEROSPACE RESEARCH LABS WRIGHTPATTERSON AFB OHIO
Personal Author(s) : McIntosh,Duncan M.
Report Date : NOV 1969
Pagination or Media Count : 141
Abstract : The modern methods of the Calculus of Variations are used to find the primary necessary conditions for optimal control. A general problem is formulated which involves: (1) state and control variables defined in a region R with the state variables described by partial differential equations, (2) conditions on the boundary of R which are, typically, the boundary conditions for the interior partial differential equations, and (3) algebraic equations which must hold at the corner points of the boundary of R. A standard format is developed in which a large number of problems may be stated. Once a problem is stated in this standard format the formulae obtained in the dissertation gives a complete system of partial differential equations together with boundary conditions which when solved will yield the optimal control sought. The method is equally applicable to elliptic, parabolic, and hyperbolic partial differential equations. Example problems demonstrate: (1) control within the interior of a region, (2) control using state variables on the boundary, (3) control by varying the shape of the boundary, (4) control with variables defined only on the boundary, and (5) control using quasicontrol variables. A final example demonstrates the agreement of the general method developed in the dissertation with a specific method developed by A. I. Egorov. (Author)
Descriptors : (*CONTROL SYSTEMS, *CALCULUS OF VARIATIONS), PARTIAL DIFFERENTIAL EQUATIONS, BOUNDARY VALUE PROBLEMS, CONDUCTION(HEAT TRANSFER), OPTIMIZATION, THESES
Subject Categories : Numerical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE