Fabian Wirth
Asymptotics of value functions of discrete-time discounted optimal control.
Preprint series: Report 411, Institut für Dynamische Systeme, Universität Bremen,
49N20 Periodic optimization
90C30 Nonlinear programming
We study deterministic discounted optimal control problems
associated with discrete-time systems. It is shown that for small
discount rates controllability properties of the underlying system
can guarantee the convergence of the discounted value function to
the value function of the average yield. An application in the
theory of exponential growth rates of discrete inclusions is
presented. This application motivates the analysis of the infinite
horizon optimal control problems with running yields that are
unbounded from below.

Keywords: Discrete-time, optimal control, discount rates, average yield, control sets, Lyapunov exponents