A differential game with constrained dynamics and viscosity solutions of a related HJB equation

Details A differential game with constrained dynamics and viscosity solutions of a related HJB equation A differential game with constrained dynamics and viscosity solutions of a related HJB equation

1999-07-08

arxiv.org/abs/math/9907195v1

Mathematics

Optimization and Control

Scientific paper

This paper considers a formulation of a differential game with constrained dynamics, where one player selects the dynamics and the other selects the applicable cost. When the game is considered on a finite time horizon, its value satisfies an HJB equation with oblique Neumann boundary conditions. The first main result is uniqueness for viscosity solutions to this equation. This uniqueness is applied to obtain the second main result,i which is a unique characterization of the value function for a corresponding infinite time problem. The motivation comes from problems associated with queueing networks, where the games appear in several contexts, including a robust approach to network modeling and optimization and risk-sensitive control.

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