Abstract: In a recent paper [1] we showed, among other things, how a fairly general control problem, or programming problem, with constraints can be reduced to a special type of Bolza problem in the calculus of variations. Necessary conditions for the Bolza problem were then translated into necessary conditions for optimal control. These conditions include the maximum principle of Pontryagin [2, 3] for this class of problems and some of the later results of Gamkrelidze [4]. Our results in [1] do not, however, apply to control problems with constraints on the state variables that do not explicitly involve the control variable. Such problems were treated by Gamkrelidze in [4], who modified the arguments in [2] to account for the additional constraints. In this memorandum we shall use the methods of [1] to study such problems, and we shall obtain the results of Gamkrelidze, with one exception, from relevant results in the calculus of variations.
Keywords: Optimal Control, Constraints, Peacewise smooth boundary, Modification, Interior, Restriction.
Title: On Control Problems with Bounded State Variables
Author: Dr. Bishmbher Dayal
International Journal of Engineering Research and Reviews
ISSN 2348-697X (Online)
Vol. 11, Issue 1, January 2023 - March 2023
Page No: 10-19
Research Publish Journals
Website: www.researchpublish.com
Published Date: 09-February-2023
