Back to Search
Start Over
Control on Hilbert Spaces and Application to Some Mean Field Type Control Problems
- Publication Year :
- 2020
- Publisher :
- arXiv, 2020.
-
Abstract
- We propose a new approach to studying classical solutions of the Bellman equation and Master equation for mean field type control problems, using a novel form of the "lifting" idea introduced by P.-L. Lions. Rather than studying the usual system of Hamilton-Jacobi/Fokker-Planck PDEs using analytic techniques, we instead study a stochastic control problem on a specially constructed Hilbert space, which is reminiscent of a tangent space on the Wasserstein space in optimal transport. On this Hilbert space we can use classical control theory techniques, despite the fact that it is infinite dimensional. A consequence of our construction is that the mean field type control problem appears as a special case. Thus we preserve the advantages of the lifiting procedure, while removing some of the difficulties. Our approach extends previous work by two of the coauthors, which dealt with a deterministic control problem for which the Hilbert space could be generic.
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....a87ba3cd5a07e97ddce02471de3cd837
- Full Text :
- https://doi.org/10.48550/arxiv.2005.10770