Foundations of the Calculus of Variations and Optimal Control

  • Terry L. Friesz
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 135)


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.


Optimal Control Problem Optimal Control Theory Minimum Principle Terminal Time Adjoint Variable 
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List of References Cited and Additional Reading

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Dept. Industrial & Manufacturing EngineeringPennsylvania State UniversityUniversity ParkUSA

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