University of Illinois at Urbana-Champaign
On the Smoothness of the Bellman Function
Abstract
dc:descriptionIn Optimal Control Theory, necessary and sufficient conditions for the optimality of a given control, under the assumption that the Bellman function is continously differentiable, can be established by the method of dynamic programming. However, as simple examples show, the Bellman function is in general not differentiable everywhere on the attainable set. Boltyanskii introduced the concept of a regular synthesis for a control system which subsequently leads to the proof that the Bellman function is continously differentiable on an open and dense subset of the attainable set. The existence of regular syntheses for various control systems has since been established by Brunovsky and Sussmann. The works of these authors rely heavily on results from the theory of subanalytic sets due to Hardt and Hironaka.
Degree
thesis:*- Name thesis:degree_name
- Ph.D.
- Level thesis:degree_level
- Dissertation
- Discipline thesis:degree_discipline
- Mathematics
- Grantor
- University of Illinois at Urbana-Champaign
- Year dc:date
- 2014
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Tanner, Franz Xaver
- Contributors dc:contributor
-
- Albrecht, Felix
Subjects
dc:subject × 1Identifiers
dc:identifier.*- Identifier
- (UMI)AAI8908864
- OAI identifier oai:identifier
- oai:www.ideals.illinois.edu:2142/71272