Optimal control of first-order Hamilton-Jacobi equations with linearly bounded Hamiltonian - Inria - Institut national de recherche en sciences et technologies du numérique
Preprints, Working Papers, ... Year : 2013

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

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

Dates and versions

hal-00871964 , version 1 (11-10-2013)

Identifiers

Cite

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

Altmetric

Share

More