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

Anup Biswas, Hitoshi Ishii, Subhamay Saha, Lin Wang

    Research output: Contribution to journalArticle

    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 languageEnglish
    Pages (from-to)365-396
    Number of pages32
    JournalSIAM Journal on Control and Optimization
    Volume55
    Issue number1
    DOIs
    Publication statusPublished - 2017

    Fingerprint

    HJB Equation
    State Constraints
    Viscosity Solutions
    Value Function
    Viscosity
    Control Problem
    Queueing networks
    Queueing Networks
    Unique Solution
    Euclidean space
    Non-negative
    Boundary conditions
    Face

    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

    Cite this

    On viscosity solution of hjb equations with state constraints and reflection control. / Biswas, Anup; Ishii, Hitoshi; Saha, Subhamay; Wang, Lin.

    In: SIAM Journal on Control and Optimization, Vol. 55, No. 1, 2017, p. 365-396.

    Research output: Contribution to journalArticle

    Biswas, Anup ; Ishii, Hitoshi ; Saha, Subhamay ; Wang, Lin. / On viscosity solution of hjb equations with state constraints and reflection control. In: SIAM Journal on Control and Optimization. 2017 ; Vol. 55, No. 1. pp. 365-396.
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