Issue ESAIM: COCV Volume 12, Number 4, October 2006 Page(s) 662 - 698 DOI 10.1051/cocv:2006016 Published online 11 October 2006

ESAIM: COCV, October 2006, Vol. 12, pp. 662-698
DOI: 10.1051/cocv:2006016

Boundary-influenced robust controls: two network examples

Martin V. Day

Department of Mathematics, Virginia Tech, Blacksburg, Virginia 24061-0123 USA; day@math.vt.edu

(Received February 10, 2005. Revised June 5, 2005. Published online 11 October 2006.)

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.

Mathematics Subject Classification. 49L25, 49N70, 90C39, 91A23, 93C15.

Key words: Robust control, differential game, queueing network.


© EDP Sciences, SMAI 2006

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