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

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

11 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
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	4737-4742
Number of pages	6
ISBN (Print)	1424414989, 9781424414987
DOIs	https://doi.org/10.1109/CDC.2007.4434060
State	Published - 2007
Externally published	Yes
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)	0743-1546
ISSN (Electronic)	2576-2370

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

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10.1109/CDC.2007.4434060

Cite this

Bayen, A. M., 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 (pp. 4737-4742). Article 4434060 (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2007.4434060

Bayen, Alexandre M. ; Claudel, Christian ; Saint-Pierre, Patrick. / Computation of solutions to the Moskowitz Hamilton-Jacobi-Bellman equation under viability constraints. Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC. Institute of Electrical and Electronics Engineers Inc., 2007. pp. 4737-4742 (Proceedings of the IEEE Conference on Decision and Control).

@inproceedings{ea8a0ed63e11452fb5974b4b39134632,

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",

doi = "10.1109/CDC.2007.4434060",

language = "English (US)",

isbn = "1424414989",

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

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "4737--4742",

booktitle = "Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC",

address = "United States",

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

}

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, Institute of Electrical and Electronics Engineers Inc., 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. Institute of Electrical and Electronics Engineers Inc., 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

TY - GEN

T1 - Computation of solutions to the Moskowitz Hamilton-Jacobi-Bellman equation under viability constraints

AU - Bayen, Alexandre M.

AU - Claudel, Christian

AU - Saint-Pierre, Patrick

PY - 2007

Y1 - 2007

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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U2 - 10.1109/CDC.2007.4434060

DO - 10.1109/CDC.2007.4434060

M3 - Conference contribution

AN - SCOPUS:55549111666

SN - 1424414989

SN - 9781424414987

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 4737

EP - 4742

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

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 46th IEEE Conference on Decision and Control 2007, CDC

Y2 - 12 December 2007 through 14 December 2007

ER -

Bayen AM, Claudel C, Saint-Pierre P. 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. Institute of Electrical and Electronics Engineers Inc. 2007. p. 4737-4742. 4434060. (Proceedings of the IEEE Conference on Decision and Control). doi: 10.1109/CDC.2007.4434060

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

Abstract

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