François Lamoline (UNamur)

Title: Well-Posedness of Boundary Controlled and Observed Stochastic Port-Hamiltonian systems

Abstract: On finite-dimensional spaces, the well-posedness is not a concern and is usually not even mentioned. However, on infinite-dimensional spaces, establishing the well-posedness is of paramount importance and paves the way for dealing with control/estimation, transfer function, etc. In this talk, stochastic port-Hamiltonian systems on infinite-dimensional spaces governed by Ito stochastic differential equations and with boundary control and observation operators 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.