On the Optimal Control Problem With Unrestricted Final Time

[+] Author and Article Information
C. T. Leondes, R. A. Niemann

California State College at Los Angeles, Los Angeles, Calif.

J. Basic Eng 91(2), 155-160 (Jun 01, 1969) (6 pages) doi:10.1115/1.3571051 History: Received December 17, 1968; Online November 03, 2011


In problems of optimal control, the final time T may be fixed or it may be unrestricted. For the unrestricted final time case, an additional necessary condition that the Hamiltonian be zero is added to the conditions for optimality used for the fixed time case. In this paper, it will be shown that this necessary condition may lead to a local maximum of the performance criterion with respect to final times as well as a local minimum. This paper first develops a computational algorithm using only the H = 0 condition, and then develops a sufficient condition for a local minimum with respect to final time and a computational algorithm employing this condition. Numerical examples are given to illustrate all results.

Copyright © 1969 by ASME
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