A new formulation of state constraint problems for first-order PDES

Hitoshi Ishii; Shigeaki Koike

doi:10.1137/S0363012993250268

A new formulation of state constraint problems for first-order PDES

Hitoshi Ishii, Shigeaki Koike

Research output: Contribution to journal › Article

47 Citations (Scopus)

Abstract

The first-order Hamilton-Jacobi-Bellman equation associated with the state constraint problem for optimal control is studied. Instead of the boundary condition which Soner introduced, a new and appropriate boundary condition for the PDE is proposed. The uniqueness and Lipschitz continuity of viscosity solutions for the boundary value problem are obtained.

Original language	English
Pages (from-to)	554-571
Number of pages	18
Journal	SIAM Journal on Control and Optimization
Volume	34
Issue number	2
DOIs	https://doi.org/10.1137/S0363012993250268
Publication status	Published - 1996 Mar
Externally published	Yes

Keywords

Comparison principle
State constraint problem
Viscosity solution

ASJC Scopus subject areas

Control and Optimization
Applied Mathematics

Access to Document

10.1137/S0363012993250268

Fingerprint Dive into the research topics of 'A new formulation of state constraint problems for first-order PDES'. Together they form a unique fingerprint.

Cite this

Ishii, H., & Koike, S. (1996). A new formulation of state constraint problems for first-order PDES. SIAM Journal on Control and Optimization, 34(2), 554-571. https://doi.org/10.1137/S0363012993250268

@article{939a21053dba47f089054059f981ca75,

title = "A new formulation of state constraint problems for first-order PDES",

abstract = "The first-order Hamilton-Jacobi-Bellman equation associated with the state constraint problem for optimal control is studied. Instead of the boundary condition which Soner introduced, a new and appropriate boundary condition for the PDE is proposed. The uniqueness and Lipschitz continuity of viscosity solutions for the boundary value problem are obtained.",

keywords = "Comparison principle, State constraint problem, Viscosity solution",

author = "Hitoshi Ishii and Shigeaki Koike",

year = "1996",

month = mar,

doi = "10.1137/S0363012993250268",

language = "English",

volume = "34",

pages = "554--571",

journal = "SIAM Journal on Control and Optimization",

issn = "0363-0129",

publisher = "Society for Industrial and Applied Mathematics Publications",

number = "2",

}

TY - JOUR

T1 - A new formulation of state constraint problems for first-order PDES

AU - Ishii, Hitoshi

AU - Koike, Shigeaki

PY - 1996/3

Y1 - 1996/3

N2 - The first-order Hamilton-Jacobi-Bellman equation associated with the state constraint problem for optimal control is studied. Instead of the boundary condition which Soner introduced, a new and appropriate boundary condition for the PDE is proposed. The uniqueness and Lipschitz continuity of viscosity solutions for the boundary value problem are obtained.

AB - The first-order Hamilton-Jacobi-Bellman equation associated with the state constraint problem for optimal control is studied. Instead of the boundary condition which Soner introduced, a new and appropriate boundary condition for the PDE is proposed. The uniqueness and Lipschitz continuity of viscosity solutions for the boundary value problem are obtained.

KW - Comparison principle

KW - State constraint problem

KW - Viscosity solution

UR - http://www.scopus.com/inward/record.url?scp=0030107199&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030107199&partnerID=8YFLogxK

U2 - 10.1137/S0363012993250268

DO - 10.1137/S0363012993250268

M3 - Article

AN - SCOPUS:0030107199

VL - 34

SP - 554

EP - 571

JO - SIAM Journal on Control and Optimization

JF - SIAM Journal on Control and Optimization

SN - 0363-0129

IS - 2

ER -