Boundary-influenced robust controls: two network examples

Martin V. Day

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

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

Abstract

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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.

How to cite

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Day, 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 -

References

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