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Dynamic Optimization and Differential Games pp 79–146Cite as

Foundations of the Calculus of Variations and Optimal Control

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Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 135))

Abstract

In this chapter, we treat time as a continuum and derive optimality conditions for the extremization of certain functionals.We consider both variational calculus problems that are not expressed as optimal control problems and optimal control problems themselves. In this chapter, we relie on the classical notion of the variation of a functional. This classical perspective is the fastest way to obtain useful results that allow simple example problems to be solved that bolster one’s understanding of continuous-time dynamic optimization.

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Author information

Authors and Affiliations

  1. Dept. Industrial & Manufacturing Engineering, Pennsylvania State University, 305 Leonhard Building, University Park, Pennsylvania, 16802, USA

    Terry L. Friesz

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  1. Terry L. Friesz
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Correspondence to Terry L. Friesz .

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Friesz, T.L. (2010). Foundations of the Calculus of Variations and Optimal Control. In: Dynamic Optimization and Differential Games. International Series in Operations Research & Management Science, vol 135. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-72778-3_3

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