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

Indian Institute of Science Education and Research Pune
Waseda University
Indian Institute of Technology Guwahati
Tsinghua University

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

4 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
Externally published	Yes

Keywords

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

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10.1137/15M103830X

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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",

note = "Publisher Copyright: {\textcopyright} 2017 Society for Industrial and Applied Mathematics.",

year = "2017",

doi = "10.1137/15M103830X",

language = "English",

volume = "55",

pages = "365--396",

journal = "SIAM Journal on Control and Optimization",

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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 - https://www.scopus.com/pages/publications/85014396510

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

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