We consider the differential game associated with robust control of asystem in a compact state domain, using Skorokhod dynamics on theboundary. A specific class of problems motivated by queueing network controlis considered. A constructive approach to the Hamilton-Jacobi-Isaacsequation is developed which is based on an appropriate family ofextremals, including boundary extremals for which the Skorokhoddynamics are active. A number of technical lemmas and a structuredverification theorem are formulated to support the use of thistechnique in simple examples. Two examples are considered whichillustrate the application of the results. This extends previous workby Ball, Day and others on such problems, but with a new emphasis onproblems for which the Skorokhod dynamics play a critical role. Connections with the viscosity-sense oblique derivative conditions ofLions and others are noted.
