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

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

52 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

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10.1137/S0363012993250268

Cite this

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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",

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AU - Ishii, Hitoshi

AU - Koike, Shigeaki

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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

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JF - SIAM Journal on Control and Optimization

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ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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