OPTIMUM CONTROL OF DISTRIBUTED PARAMETER SYSTEMS WITH TWO INDEPENDENT VARIABLES.
AEROSPACE RESEARCH LABS WRIGHT-PATTERSON AFB OHIO
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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 quasi-control 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
- Numerical Mathematics