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Computational Methods in Optimal Control Problems

Report Number: AFFDL TR 65-50
Author(s): James A. Payne
Corporate Author: University of California Department of Engineering
Laboratory: Air Force Flight Dynamics Laboratory
Date of Publication: 1965-08
Pages: 134
Contract: AF 33(615)-1794
Project: 8225
Task: 822501
AD Number: AD0622081

This report considers the application of optimization techniques to the development of methods for the control of engineering systems. The systems considered are those physical processes which are subject to independent control forces and in which the dynamics of the process are of central importance. It is assumed that the process can be described by a system of ordinary nonlinear differential equations. The optimization, with respect to a general criterion function, of such systems is considered. The conditions and equations which specify the optimal system behavior are derived by means of the Maximum Principle. System trajectories which satisfy the optimal conditions, i.e., optimal trajectories, can only be obtained by numerical computation. Various approaches to this computational problem are reviewed and their primary limitations are discussed. In order to provide a realistic evaluation of certain computational methods, the optimization of a particular engineering system is considered in detail. This system is a variable lift aerodynamic vehicle during the atmospheric reentry phase. A mathematical model for this system is developed and the optimization of this model is considered. The criterion function is a linear combination of the heating and acceleration effects which are experienced by the vehicle during the reentry phase.

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