Résumé
In this article, Stochastic port-Hamiltonian systems (SPHS) on infinite-dimensional spaces governed by Itô stochastic differential equations (SDEs) are introduced, and some properties of this new class of systems are studied. They are an extension of SPHSs defined on a finite-dimensional state space. The concept of well-posedness in the sense of Weiss and Salamon is generalized to the stochastic context. Under this extended definition, SPHSs are shown to be well posed. The theory is illustrated on an example of a vibrating string subject to a Hilbert space-valued Gaussian white noise process.
| langue originale | Anglais |
|---|---|
| Numéro d'article | 8906170 |
| Pages (de - à) | 4258-4264 |
| Nombre de pages | 7 |
| journal | IEEE Transactions on Automatic Control |
| Volume | 65 |
| Numéro de publication | 10 |
| Les DOIs | |
| Etat de la publication | Publié - oct. 2020 |
Financement
Manuscript received January 8, 2019; revised July 12, 2019; accepted November 6, 2019. Date of publication November 19, 2019; date of current version September 25, 2020. This work was supported by F.R.S-FNRS. The work of F. Lamoline was supported by FRIA under Grant F 3/5/5-MCF/BC. Recommended by Associate Editor Prof. Y. L. Gorrec. (Corresponding author: Francois Lamoline.) The authors are with the Department of Mathematics, University of Namur and Namur Institute for Complex Systems, B-5000 Namur, Belgium (e-mail: [email protected]; joseph.winkin @unamur.be). Digital Object Identifier 10.1109/TAC.2019.2954481