✍ Scribed by Lars Grüne; Fabian Wirth
No coin nor oath required. For personal study only.
In this paper we investigate the rate of convergence of the optimal value function of an inÿnite 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 quadratic pointwise convergence. From this we derive under appropriate controllability conditions criteria for linear uniform convergence of the value functions on control sets. Applications of these results are given and an example is discussed in which both linear and slower rates of convergence occur depending on the cost functional.
📜 SIMILAR VOLUMES
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