# On linear convergence of discounted optimal control problems with vanishing discount rate

L. Grüne, F. Wirth:
**On linear convergence of discounted optimal control problems with vanishing discount rate**

in:
*Proceedings of the Mathematical Theory of Networks and Systems (MTNS98),*
*
*
Padova,
1998,
185 - 188

## Abstract:

In this paper we investigate the rate of convergence of the optimal value function of an infinite horizon discounted optimal control problem as the discount rate tends to zero. We provide several estimates along trajectories yielding results on the rate of convergence of the corresponding functional. Using appropriate controllability assumptions we derive a linear convergence theorem on control sets. Applications of these results are given and an example is discussed in which both linear and slower rates of convergence occur.