Convex optimization formulation of estimation problems involving Hamilton-Jacobi equations. Applications to traffic flow estimation

Christian Claudel
King Abdullah University of Science and Technology (KAUST)

This talk describes a new method for solving inverse modeling problems in systems modeled by conservation laws, with applications to highway traffic flow estimation. The state of the system is written in the form of a scalar Hamilton-Jacobi (HJ) partial differential equation
(PDE), for which the solution is fully characterized by a Lax-Hopf formula. Using the properties of the solution, we prove that when the data of the problem is prescribed in piecewise affine form, the constraints of the model are convex. This property enables us to identify a class of inverse modeling problems that can be formulated using convex programs

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