A stochastic control problem over an infinite horizon which involves a linear system and a convex cost functional is analyzed. We prove the convergence of the dynamic programming algorithm associated with the problem, and we show the existence of a stationary Borel measurable optimal control law. The approach used illustrates how results on infinite time reachability  can be used for the analysis of dynamic programming algorithms over an infinite horizon subject to state constraints.
ASJC Scopus subject areas
- Control and Systems Engineering
- Computer Science Applications
- Electrical and Electronic Engineering