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Article Dans Une Revue ESAIM: Control, Optimisation and Calculus of Variations Année : 2023

A General Comparison Principle for Hamilton Jacobi Bellman Equations on Stratified Domains

Résumé

This manuscript aims to study finite horizon, first order Hamilton Jacobi Bellman (HJB) equations on stratified domains. This problem is related to optimal control problems with discontinuous dynamics. We use nonsmooth analysis techniques to derive a strong comparison principle as in the classical theory and deduce that the value function is the unique viscosity solution. Furthermore, we prove some stability results of the Hamilton Jacobi Bellman equation. Finally, we establish a general convergence result for monotone numerical schemes in the stratified case.
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Dates et versions

hal-03408797 , version 1 (29-10-2021)
hal-03408797 , version 2 (10-01-2023)

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Othmane Jerhaoui, Hasnaa Zidani. A General Comparison Principle for Hamilton Jacobi Bellman Equations on Stratified Domains. ESAIM: Control, Optimisation and Calculus of Variations, 2023, 29, ⟨10.1051/cocv/2022089⟩. ⟨hal-03408797v2⟩
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