Investigation of Optimal Control With a Minimum-Fuel Consumption Criterion for a Fourth-Order Plant With Two Control Inputs; Synthesis of an Efficient Suboptimal Control

[+] Author and Article Information
A. J. Craig

Department of Aeronautical Engineering, Wichita State University, Wichita, Kan.

I. Flügge-Lotz

Stanford University, Stanford, Calif.

J. Basic Eng 87(1), 39-57 (Mar 01, 1965) (19 pages) doi:10.1115/1.3650527 History: Received April 23, 1964; Online November 03, 2011


Application of Pontryagin’s optimal principle to control system problems eventually requires that a two-point boundary-value problem be solved. For plants whose equations of motion are greater than second order this represents a formidable barrier in realizing a practical feedback control. When the criterion for optimization is minimum-fuel consumption, choice of time for solution may be used as a free parameter, and this plus consideration of the efficiency of application of control leads to an approximate method which avoids this difficulty. A heuristic analysis of the geometry of state-space trajectories, using true optimal solutions as a guide, provides laws for constructing a feedback control from the state variables. It further provides a knowledge of the bounds of performance of the mechanized suboptimal control and an estimate on the performance of a minimum-time control for comparison purposes. As an example, the method is applied to the problem of minimum-fuel attitude control of an earth-orbiting satellite, a fourth-order plant with two controls.

Copyright © 1965 by ASME
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