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

摘要

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