On viscosity solution of hjb equations with state constraints and reflection control

Anup Biswas; Hitoshi Ishii; Subhamay Saha; Lin Wang

doi:10.1137/15M103830X

On viscosity solution of hjb equations with state constraints and reflection control

Anup Biswas, Hitoshi Ishii, Subhamay Saha, Lin Wang

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

2 Citations (Scopus)

Abstract

Motivated by a control problem of a certain queueing network we consider a control problem where the dynamics is constrained in the nonnegative orthant Rd + of the d-dimensional Euclidean space and controlled by the reections at the faces/boundaries. We define a discounted value function associated to this problem and show that the value function is a viscosity solution to a certain HJB equation in Rd + with nonlinear Neumann type boundary condition. Under certain conditions, we also characterize this value function as the unique solution to this HJB equation.

Original language	English
Pages (from-to)	365-396
Number of pages	32
Journal	SIAM Journal on Control and Optimization
Volume	55
Issue number	1
DOIs	https://doi.org/10.1137/15M103830X
Publication status	Published - 2017

Keywords

Heavy-trafic
Nonlinear Neumann boundary
Nonsmooth domain
Queues with help
Skorokhod map with reection control
Stochastic network
Viscosity solutions

ASJC Scopus subject areas

Control and Optimization
Applied Mathematics

Access to Document

10.1137/15M103830X

Cite this

@article{5492d321bd0b461ea5b783b9122dbc0f,

title = "On viscosity solution of hjb equations with state constraints and reflection control",

abstract = "Motivated by a control problem of a certain queueing network we consider a control problem where the dynamics is constrained in the nonnegative orthant Rd + of the d-dimensional Euclidean space and controlled by the reections at the faces/boundaries. We define a discounted value function associated to this problem and show that the value function is a viscosity solution to a certain HJB equation in Rd + with nonlinear Neumann type boundary condition. Under certain conditions, we also characterize this value function as the unique solution to this HJB equation.",

keywords = "Heavy-trafic, Nonlinear Neumann boundary, Nonsmooth domain, Queues with help, Skorokhod map with reection control, Stochastic network, Viscosity solutions",

author = "Anup Biswas and Hitoshi Ishii and Subhamay Saha and Lin Wang",

year = "2017",

doi = "10.1137/15M103830X",

language = "English",

volume = "55",

pages = "365--396",

journal = "SIAM Journal on Control and Optimization",

issn = "0363-0129",

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

number = "1",

}

TY - JOUR

T1 - On viscosity solution of hjb equations with state constraints and reflection control

AU - Biswas, Anup

AU - Ishii, Hitoshi

AU - Saha, Subhamay

AU - Wang, Lin

PY - 2017

Y1 - 2017

N2 - Motivated by a control problem of a certain queueing network we consider a control problem where the dynamics is constrained in the nonnegative orthant Rd + of the d-dimensional Euclidean space and controlled by the reections at the faces/boundaries. We define a discounted value function associated to this problem and show that the value function is a viscosity solution to a certain HJB equation in Rd + with nonlinear Neumann type boundary condition. Under certain conditions, we also characterize this value function as the unique solution to this HJB equation.

AB - Motivated by a control problem of a certain queueing network we consider a control problem where the dynamics is constrained in the nonnegative orthant Rd + of the d-dimensional Euclidean space and controlled by the reections at the faces/boundaries. We define a discounted value function associated to this problem and show that the value function is a viscosity solution to a certain HJB equation in Rd + with nonlinear Neumann type boundary condition. Under certain conditions, we also characterize this value function as the unique solution to this HJB equation.

KW - Heavy-trafic

KW - Nonlinear Neumann boundary

KW - Nonsmooth domain

KW - Queues with help

KW - Skorokhod map with reection control

KW - Stochastic network

KW - Viscosity solutions

UR - http://www.scopus.com/inward/record.url?scp=85014396510&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85014396510&partnerID=8YFLogxK

U2 - 10.1137/15M103830X

DO - 10.1137/15M103830X

M3 - Article

AN - SCOPUS:85014396510

SN - 0363-0129

VL - 55

SP - 365

EP - 396

JO - SIAM Journal on Control and Optimization

JF - SIAM Journal on Control and Optimization

IS - 1

ER -

On viscosity solution of hjb equations with state constraints and reflection control

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this