In an optimal control framework, we consider the value VT(x) of the problem starting from state x with finite horizon T, as well as the value W λ(x) of the λ-discounted problem starting from x. We prove that uniform convergence (on the set of states) of the values VT(⋅) as T tends to infinity is equivalent to uniform convergence of the values W λ(⋅) as λ tends to 0, and that the limits are identical. An example is also provided to show that the result does not hold for pointwise convergence. This work is an extension, using similar techniques, of a related result by Lehrer and Sorin in a discrete-time framework.
CITATION STYLE
Oliu-Barton, M., & Vigeral, G. (2013). A uniform tauberian theorem in optimal control. In Annals of the International Society of Dynamic Games (Vol. 12, pp. 199–215). Birkhauser. https://doi.org/10.1007/978-0-8176-8355-9_10
Mendeley helps you to discover research relevant for your work.