Control theory on Wasserstein space : a new approach to optimality conditions
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review
Author(s)
Related Research Unit(s)
Detail(s)
| Original language | English |
|---|---|
| Pages (from-to) | 565-628 |
| Journal / Publication | Annals of Mathematical Sciences and Applications |
| Volume | 8 |
| Issue number | 3 |
| Online published | 14 Nov 2023 |
| Publication status | Published - 2023 |
Link(s)
| DOI | DOI |
|---|---|
| Permanent Link | https://scholars.cityu.edu.hk/en/publications/publication(424f3e37-9cab-434f-9a76-0dd6cb97f56a).html |
Abstract
We study the deterministic control problem in the Wasserstein space, following the recent works of Bonnet and Frankowska, but with a new approach. One of the major advantages of our approach is that it reconciles the closed loop and the open loop approaches, without the technicalities of the traditional feedback control methodology. It allows also to embed the control problem in the Wasserstein space into a control problem in a Hilbert space, similar to the lifting method introduced by P. L. Lions, used already in our previous works. The Hilbert space is different from that proposed by P. L. Lions, and it allows to recover the control problem in the Wasserstein space as a particular case.
Research Area(s)
- Mean field type control problem, Wasserstein space, Hilbert space, Pontryagin maximum principle, forward-backward equations, value function, Bellman equation
Citation Format(s)
Control theory on Wasserstein space: a new approach to optimality conditions. / BENSOUSSAN, Alain; HUANG, Ziyu; YAM, Sheung Chi Phillip.
In: Annals of Mathematical Sciences and Applications, Vol. 8, No. 3, 2023, p. 565-628.
In: Annals of Mathematical Sciences and Applications, Vol. 8, No. 3, 2023, p. 565-628.
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review
