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Variational Principles

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Optimal Control

Part of the book series: Modern Birkhäuser Classics ((MBC))

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Abstract

The Name “variational principle” is traditionally attached to a law of nature asserting that some quantity is minimized. Examples are Dirichlet’s Principle (the spatial distribution of an electrostatic field minimizes some quadratic functional), Fermat’s Principle (a light ray follows a shortest path), or Hamilton’s Principle of Least Action (the evolution of a dynamical system is an “extremum” for the action functional). These principles are called “variational” because working through their detailed implications entails solving problems in the Calculus of Variations.

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  1. Department of Electrical Engineering, Imperial College of Science, Technology, and Medicine, London, SW7 2BT, UK

    Richard Vinter

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Vinter, R. (2010). Variational Principles. In: Optimal Control. Modern Birkhäuser Classics. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-8086-2_3

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