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Boundary-influenced robust controls: two network examples

Published online by Cambridge University Press:  11 October 2006

Martin V. Day
Martin V. Day*
Affiliation:
Department of Mathematics, Virginia Tech, Blacksburg, Virginia 24061-0123 USA; day@math.vt.edu
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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.

Keywords

Robust controldifferential gamequeueing network.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 12 , Issue 4 , October 2006 , pp. 662 - 698
Copyright
© EDP Sciences, SMAI, 2006

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