SIAM Journal on Control and Optimization, Vol.55, No.1, 365-396, 2017
ON VISCOSITY SOLUTION OF HJB EQUATIONS WITH STATE CONSTRAINTS AND REFLECTION CONTROL
Motivated by a control problem of a certain queueing network we consider a control problem where the dynamics is constrained in the nonnegative orthant R-+(d) of the d-dimensional Euclidean space and controlled by the reflections at the faces/boundaries. We define a discounted value function associated to this problem and show that the value function is a viscosity solution to a certain HJB equation in R-+(d) with nonlinear Neumann type boundary condition. Under certain conditions, we also characterize this value function as the unique solution to this HJB equation.
Keywords:Skorokhod map with reflection control;queues with help;viscosity solutions;nonlinear Neumann boundary;nonsmooth domain;heavy-traffic;stochastic network