  In the last decades, control problems with infinite horizons and discount
factors have become increasingly central not only for economics but also for
applications in artificial intelligence and machine learning. The strong links
between reinforcement learning and control theory have led to major efforts
towards the development of algorithms to learn how to solve constrained control
problems. In particular, discount plays a role in addressing the challenges
that come with models that have unbounded disturbances. Although algorithms
have been extensively explored, few results take into account time-dependent
state constraints, which are imposed in most real-world control applications.
For this purpose, here we investigate feasibility and sufficient conditions for
Lipschitz regularity of the value function for a class of discounted infinite
horizon optimal control problems subject to time-dependent constraints. We
focus on problems with data that allow nonautonomous dynamics, and Lagrangian
and state constraints that can be unbounded with possibly nonsmooth boundaries.
