On the rate of convergence of infinite horizon discounted optimal value functions (Q5933582)

The authors 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 transforms the authors provide conditions on averaged functionals along suitable trajectories yielding quadratic pointwise convergence. From that the authors derive under appropriate controllability conditions criteria for linear uniform convergence of the value functions and control sets. Applications of those results are given and an example is discussed in which both linear and slower rates of convergence occur depending on the cost functional.