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
UMA - Unité de Mathématiques Appliquées, Inria Saclay - Ile de France, CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
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.
Complete list of metadatas

Cited literature [24 references]  Display  Hide  Download

https://hal.inria.fr/hal-00820273
Contributor : Hasnaa Zidani <>
Submitted on : Friday, May 3, 2013 - 3:31:17 PM
Last modification on : Monday, September 30, 2019 - 10:46:02 AM
Long-term archiving on : Tuesday, April 4, 2017 - 4:38:19 AM

File

Rao-Siconolfi-Zidani2013.pdf
Files produced by the author(s)

Identifiers

Citation

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⟩

Share

Metrics

Record views

823

Files downloads

507