English

Well-posedness of Stochastic Port-Hamiltonian Systems on Infinite-dimensional Spaces

Optimization and Control 2019-07-10 v1

Abstract

Stochastic port-Hamiltonian systems on infinite-dimensional spaces governed by It\^o stochastic differential equations (SDEs) are introduced and some properties of this new class of systems are studied. They are an extension of stochastic port-Hamiltonian systems 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, stochastic port-Hamiltonian systems 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.

Keywords

Cite

@article{arxiv.1907.04158,
  title  = {Well-posedness of Stochastic Port-Hamiltonian Systems on Infinite-dimensional Spaces},
  author = {François Lamoline and Joseph J. Winkin},
  journal= {arXiv preprint arXiv:1907.04158},
  year   = {2019}
}