Abstract
Motivated by a control problem of a certain queueing network we consider a control problem where the dynamics is constrained in the nonnegative orthant Rd + of the d-dimensional Euclidean space and controlled by the reections 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 Rd + with nonlinear Neumann type boundary condition. Under certain conditions, we also characterize this value function as the unique solution to this HJB equation.
| Original language | English |
|---|---|
| Pages (from-to) | 365-396 |
| Number of pages | 32 |
| Journal | SIAM Journal on Control and Optimization |
| Volume | 55 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2017 |
| Externally published | Yes |
Keywords
- Heavy-trafic
- Nonlinear Neumann boundary
- Nonsmooth domain
- Queues with help
- Skorokhod map with reection control
- Stochastic network
- Viscosity solutions
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Biswas, A., Ishii, H., Saha, S., & Wang, L. (2017). On viscosity solution of hjb equations with state constraints and reflection control. SIAM Journal on Control and Optimization, 55(1), 365-396. https://doi.org/10.1137/15M103830X