Computation of solutions to the Moskowitz Hamilton-Jacobi-Bellman equation under viability constraints

Alexandre M. Bayen; Christian Claudel; Patrick Saint-Pierre

doi:10.1109/CDC.2007.4434060

Computation of solutions to the Moskowitz Hamilton-Jacobi-Bellman equation under viability constraints

Alexandre M. Bayen, Christian Claudel^*, Patrick Saint-Pierre

^*Corresponding author for this work

Computer, Electrical and Mathematical Sciences and Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

10 Scopus citations

Abstract

This article proposes a new capture basin algorithm for computing the numerical solution of a class of Hamilton-Jacobi-Bellman (HJB) partial differential equations (PDEs), based on a Lax-Hopf formula. The capture basin algorithm is derived and implemented to perform numerical computations of constrained solutions. The rate of convergence of this first order algorithm is assessed experimentally using an analytical benchmark problem. Finally, its performance is measured with highway data obtained for interstate 180 in California.

Original language	English (US)
Title of host publication	Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC
Pages	4737-4742
Number of pages	6
DOIs	https://doi.org/10.1109/CDC.2007.4434060
State	Published - Dec 1 2007
Event	46th IEEE Conference on Decision and Control 2007, CDC - New Orleans, LA, United States Duration: Dec 12 2007 → Dec 14 2007

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0191-2216

Other

Other	46th IEEE Conference on Decision and Control 2007, CDC
Country/Territory	United States
City	New Orleans, LA
Period	12/12/07 → 12/14/07

ASJC Scopus subject areas

Control and Systems Engineering
Modeling and Simulation
Control and Optimization

Access to Document

10.1109/CDC.2007.4434060

Cite this

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title = "Computation of solutions to the Moskowitz Hamilton-Jacobi-Bellman equation under viability constraints",

abstract = "This article proposes a new capture basin algorithm for computing the numerical solution of a class of Hamilton-Jacobi-Bellman (HJB) partial differential equations (PDEs), based on a Lax-Hopf formula. The capture basin algorithm is derived and implemented to perform numerical computations of constrained solutions. The rate of convergence of this first order algorithm is assessed experimentally using an analytical benchmark problem. Finally, its performance is measured with highway data obtained for interstate 180 in California.",

author = "Bayen, {Alexandre M.} and Christian Claudel and Patrick Saint-Pierre",

year = "2007",

month = dec,

day = "1",

doi = "10.1109/CDC.2007.4434060",

language = "English (US)",

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series = "Proceedings of the IEEE Conference on Decision and Control",

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note = "46th IEEE Conference on Decision and Control 2007, CDC ; Conference date: 12-12-2007 Through 14-12-2007",

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Bayen, AM, Claudel, C & Saint-Pierre, P 2007, Computation of solutions to the Moskowitz Hamilton-Jacobi-Bellman equation under viability constraints. in Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC., 4434060, Proceedings of the IEEE Conference on Decision and Control, pp. 4737-4742, 46th IEEE Conference on Decision and Control 2007, CDC, New Orleans, LA, United States, 12/12/07. https://doi.org/10.1109/CDC.2007.4434060

Computation of solutions to the Moskowitz Hamilton-Jacobi-Bellman equation under viability constraints. / Bayen, Alexandre M.; Claudel, Christian; Saint-Pierre, Patrick.

Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC. 2007. p. 4737-4742 4434060 (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Saint-Pierre, Patrick

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N2 - This article proposes a new capture basin algorithm for computing the numerical solution of a class of Hamilton-Jacobi-Bellman (HJB) partial differential equations (PDEs), based on a Lax-Hopf formula. The capture basin algorithm is derived and implemented to perform numerical computations of constrained solutions. The rate of convergence of this first order algorithm is assessed experimentally using an analytical benchmark problem. Finally, its performance is measured with highway data obtained for interstate 180 in California.

AB - This article proposes a new capture basin algorithm for computing the numerical solution of a class of Hamilton-Jacobi-Bellman (HJB) partial differential equations (PDEs), based on a Lax-Hopf formula. The capture basin algorithm is derived and implemented to perform numerical computations of constrained solutions. The rate of convergence of this first order algorithm is assessed experimentally using an analytical benchmark problem. Finally, its performance is measured with highway data obtained for interstate 180 in California.

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M3 - Conference contribution

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SN - 9781424414987

T3 - Proceedings of the IEEE Conference on Decision and Control

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BT - Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC

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Y2 - 12 December 2007 through 14 December 2007

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Computation of solutions to the Moskowitz Hamilton-Jacobi-Bellman equation under viability constraints

Abstract

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