Optimal control of scalar one-dimensional conservation laws

Abstract : This paper presents an optimal control theory for scalar one-dimensional nonlinear hyperbolic partial differential equations also called conservation laws. The solution of these equations may develop discontinuities known as shock waves that forbid the use of classical variational techniques. This paper proposes to compute the first variation of the dynamics based on its weak formulation and gives an explicit formula of its solution. Adjoint calculus is then used to evaluate gradients of cost functionals that may contain the shock locations. An application to the Burgers equation is given as an illustration.
Type de document :
Communication dans un congrès
American Control Conference, IEEE ACC'06, 2006, Minneapolis, United States. 2006, 14-16 June 2006, Minneapolis (Minnesota) Etats Unis d'Amerique
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https://hal.archives-ouvertes.fr/hal-00023175
Contributeur : Patricia Reynier <>
Soumis le : jeudi 20 avril 2006 - 15:19:24
Dernière modification le : samedi 17 octobre 2015 - 01:03:36

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  • HAL Id : hal-00023175, version 1

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Denis Jacquet, M. Krstic, Carlos Canudas de Wit. Optimal control of scalar one-dimensional conservation laws. American Control Conference, IEEE ACC'06, 2006, Minneapolis, United States. 2006, 14-16 June 2006, Minneapolis (Minnesota) Etats Unis d'Amerique. 〈hal-00023175〉

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