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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2010, Volume 268, Pages 64–75
(Mi tm2876)
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This article is cited in 9 scientific papers (total in 9 papers)
The Pontryagin maximum principle and a unified theory of dynamic optimization
F. Clarke CNRS, UMR 5208, Institut Camille Jordan, Université Claude Bernard Lyon 1, Villeurbanne, France
Abstract:
The Pontryagin maximum principle is the central result of optimal control theory. In the half-century since its appearance, the underlying theorem has been generalized, strengthened, extended, proved and reinterpreted in a variety of ways. We review in this article one of the principal approaches to obtaining the maximum principle in a powerful and unified context, focusing upon recent results that represent the culmination of over thirty years of progress using the methodology of nonsmooth analysis. We illustrate the novel features of this theory, as well as its versatility, by introducing a far-reaching new theorem that bears upon the currently active subject of mixed constraints in optimal control.
Received in April 2009
Citation:
F. Clarke, “The Pontryagin maximum principle and a unified theory of dynamic optimization”, Differential equations and topology. I, Collected papers. In commemoration of the centenary of the birth of Academician Lev Semenovich Pontryagin, Trudy Mat. Inst. Steklova, 268, MAIK Nauka/Interperiodica, Moscow, 2010, 64–75; Proc. Steklov Inst. Math., 268 (2010), 58–69
Linking options:
https://www.mathnet.ru/eng/tm2876 https://www.mathnet.ru/eng/tm/v268/p64
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