Transmission conditions on interfaces for Hamilton-Jacobi-Bellman equations

Zhiping Rao 1, 2 Antonio Siconolfi 3 Hasnaa Zidani 1, 2, *
* Corresponding author
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 establish a comparison principle for a Hamilton-Jacobi-Bellman equation, more appropriately a system, related to an infinite horizon problem in presence of an interface. Namely a low dimensional subset of the state variable space where discontinuities in controlled dynamics and costs take place. Since corresponding Hamiltonians, at least for the subsolution part, do not enjoy any semicontinuity property, the comparison argument is rather based on a separation principle of the controlled dynamics across the interface. For this, we essentially use the notion of "-partition and minimal "-partition for intervals of definition of an integral trajectory.
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Zhiping Rao, Antonio Siconolfi, Hasnaa Zidani. Transmission conditions on interfaces for Hamilton-Jacobi-Bellman equations. Journal of Differential Equations, Elsevier, 2014, 257 (11), pp.3978--4014. ⟨10.1016/j.jde.2014.07.015⟩. ⟨hal-00820273⟩

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