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Day, Martin V.

Boundary-influenced robust controls: two network examples. (English) Zbl 1114.49029

ESAIM, Control Optim. Calc. Var. 12, 662-698 (2006).
Summary: 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.

Cited in 4 Documents

MSC:

49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games
49N70 Differential games and control
90C39 Dynamic programming
91A23 Differential games (aspects of game theory)
93C15 Control/observation systems governed by ordinary differential equations

Keywords:

robust control; differential game; queueing network
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References:

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