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Chapter

Existence and Other Solution Properties

Chapter

Existence and Other Solution Properties

DOI link for Existence and Other Solution Properties

Existence and Other Solution Properties book

Existence and Other Solution Properties

DOI link for Existence and Other Solution Properties

Existence and Other Solution Properties book

BySuzanne Lenhart, John T. Workman
BookOptimal Control Applied to Biological Models

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Edition 1st Edition
First Published 2007
Imprint Chapman and Hall/CRC
Pages 16
eBook ISBN 9780429138058

ABSTRACT

In the last chapter, we developed necessary conditions to solve basic optimal control problems. However, some difficulties can arise with this method. It is possible that the necessary conditions could yield multiple solution sets, only some of which are optimal controls. Further, recall that in the development of the necessary conditions, we began by assuming an optimal control exists. It is also possible that the necessary conditions could be solvable when the original optimal control problem has no solution. We expect the objective functional evaluated at the optimal state and control to give a finite answer. If this objective functional value turns out to be ∞ or −∞, we would say the problem has no solution. An example of this is given below.

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