Journal Article

Optimal control of a system governed by nonlinear Volterra integral equations with delay

CHARLES BURNAP and MOHAMMAD A. KAZEMI

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 16, issue 1, pages 73-89
Published in print March 1999 | ISSN: 0265-0754
Published online March 1999 | e-ISSN: 1471-6887 | DOI: http://dx.doi.org/10.1093/imamci/16.1.73
Optimal control of a system governed by nonlinear Volterra integral equations with delay

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In this paper we consider an optimal control problem whose states are governed by a type of nonlinear Volterra integral equation with delay. The problem includes control constraints as well as equality/inequality constraints on the terminal states. First, using Pontryagintype control variations, a maximum principle is established under a rather general set of assumptions. We show that these results immediately yield the classical Pontryagin maximum principle for a control process governed by an ordinary differential equation (with or without delay). Next, imposing suitable convexity conditions on the functions involved, we derive Mangasarian-type and Arrow-type sufficient optimality conditions.

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Subjects: Mathematics

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