On the Rate of Convergence of Infinitehorizon Discounted Optimal

In this paper we investigate the rate of convergence of the optimal value function of an innnite 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 from this we derive 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.