Optimal control of first-order Hamilton-Jacobi equations with linearly bounded Hamiltonian

Philip Jameson Graber 1, 2
2 Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées
Abstract : We consider the optimal control of solutions of first order Hamilton-Jacobi equations, where the Hamiltonian is convex with linear growth. This models the problem of steering the propagation of a front by constructing an obstacle. We prove existence of minimizers to this optimization problem as in a relaxed setting and characterize the minimizers as weak solutions to a mean field game type system of coupled partial differential equations. Furthermore, we prove existence and partial uniqueness of weak solutions to the PDE system. An interpretation in terms of mean field games is also discussed. Keywords: Hamilton-Jacobi equations, optimal control, nonlinear PDE, viscosity solutions, front propagation, mean field games
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https://hal.inria.fr/hal-00871964
Contributor : Philip Jameson Graber <>
Submitted on : Friday, October 11, 2013 - 9:50:13 AM
Last modification on : Monday, September 30, 2019 - 10:46:02 AM

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  • HAL Id : hal-00871964, version 1
  • ARXIV : 1309.7189

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Philip Jameson Graber. Optimal control of first-order Hamilton-Jacobi equations with linearly bounded Hamiltonian. 2013. ⟨hal-00871964⟩

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