# Boundary-influenced robust controls: two network examples

ESAIM: Control, Optimisation and Calculus of Variations (2006)

- Volume: 12, Issue: 4, page 662-698
- ISSN: 1292-8119

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topDay, Martin V.. "Boundary-influenced robust controls: two network examples." ESAIM: Control, Optimisation and Calculus of Variations 12.4 (2006): 662-698. <http://eudml.org/doc/249675>.

@article{Day2006,

abstract = {
We consider the differential game associated with robust control of a
system in a compact state domain, using Skorokhod dynamics on the
boundary. A specific class of problems motivated by queueing network control
is considered. A constructive approach to the Hamilton-Jacobi-Isaacs
equation is developed which is based on an appropriate family of
extremals, including boundary extremals for which the Skorokhod
dynamics are active. A number of technical lemmas and a structured
verification theorem are formulated to support the use of this
technique in simple examples. Two examples are considered which
illustrate the application of the results. This extends previous work
by Ball, Day and others on such problems, but with a new emphasis on
problems for which the Skorokhod dynamics play a critical role.
Connections with the viscosity-sense oblique derivative conditions of
Lions and others are noted.
},

author = {Day, Martin V.},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Robust control; differential game; queueing network.; robust control; queueing network},

language = {eng},

month = {10},

number = {4},

pages = {662-698},

publisher = {EDP Sciences},

title = {Boundary-influenced robust controls: two network examples},

url = {http://eudml.org/doc/249675},

volume = {12},

year = {2006},

}

TY - JOUR

AU - Day, Martin V.

TI - Boundary-influenced robust controls: two network examples

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2006/10//

PB - EDP Sciences

VL - 12

IS - 4

SP - 662

EP - 698

AB -
We consider the differential game associated with robust control of a
system in a compact state domain, using Skorokhod dynamics on the
boundary. A specific class of problems motivated by queueing network control
is considered. A constructive approach to the Hamilton-Jacobi-Isaacs
equation is developed which is based on an appropriate family of
extremals, including boundary extremals for which the Skorokhod
dynamics are active. A number of technical lemmas and a structured
verification theorem are formulated to support the use of this
technique in simple examples. Two examples are considered which
illustrate the application of the results. This extends previous work
by Ball, Day and others on such problems, but with a new emphasis on
problems for which the Skorokhod dynamics play a critical role.
Connections with the viscosity-sense oblique derivative conditions of
Lions and others are noted.

LA - eng

KW - Robust control; differential game; queueing network.; robust control; queueing network

UR - http://eudml.org/doc/249675

ER -

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