Lars Grüne, Fabian Wirth
On the rate of convergence of infinite horizon discounted optimal value functions
Preprint series: Berichte aus der Technomathematik 98-06, Universität Bremen
90C39 Dynamic programming, See also {49L20}
49M37 Nonlinear programming, See also {90C30}
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. Using the Integration Theorem for
Laplace transformations we provide conditions on averaged functionals along suitable trajectories yielding
at most quadratic pointwise convergence. Under appropriate controllability assumptions we derive from this
criteria for at most linear uniform convergence on control sets. Applications of these results are given and
an example is discussed in which both linear and slower rates of convergence occur.

Keywords: infinite horizon optimal control, value function, discount rate, convergence rate