Hamilton-Jacobi-Bellman Equations on Multi-Domains

Zhiping Rao (1, 2) , Hasnaa Zidani (1, 2)

1 Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems
2 OC - Optimisation et commande

A system of Hamilton Jacobi (HJ) equations on a partition of $\R^d$ is considered, and a uniqueness and existence result of viscosity solution is analyzed. While the notion of viscosity notion is by now well known, the question of uniqueness of solution, when the Hamiltonian is discontinuous, remains an important issue. A uniqueness result has been derived for a class of problems, where the behavior of the solution, in the region of discontinuity of the Hamiltonian, is assumed to be irrelevant and can be ignored (see reference [10]) . Here, we provide a new uniqueness result for a more general class of Hamilton-Jacobi equations.

Mots clés: Hamilton-Jacobi equations; discontinuous Hamiltonian; viscosity notion; optimal control

Domaines: Equations aux dérivées partielles [math.AP]

Zhiping Rao, Hasnaa Zidani. Hamilton-Jacobi-Bellman Equations on Multi-Domains. K. Bredies; C. Clason; K. Kunisch; G. von Winckel. Control and Optimization with PDE Constraints, 164, Springer, pp.93--116, 2013, International Series of Numerical Mathematics, 978-3-0348-0630-5. ⟨10.1007/978-3-0348-0631-2_6⟩. ⟨hal-00803108⟩