On analysis and Linear Quadratic Control of Stochastic port-Hamiltonian systems on Infinite-dimensional spaces

In this thesis, we focus on infinite-dimensional stochastic port-Hamiltonian systems. This
Hamiltonian approach allows us to consider a large range of problems involving boundary
control. The stochastic approach allows us to take account of various disturbances such as
measurement noise, modeling error and so on in controlling real plants. They sometimes
may cause performance degradation and even destabilization of the plant system. The
stochastic control is an efficient way to consider them. It is expected that the stochastic-
Hamiltonian approach will lead hopefully to a minimisation of the model errors.
The research project aims to study the resolution of the LQG control problem for infinitedimensional
stochastic port-Hamiltonian systems. The initial interest is to develop a more
appropriate analysis than the semigroup approach. First of all, stochastic port-Hamiltonian
systems and the balance equation will be defined and some of the properties of these
dynamical systems will be clarified. To the author's knowledge, the extension in infinitedimensional
space has not been made yet. Next, the Kalman filter for this class of systems
will be studied. The aim is to estimate the state of the plant system. Eventually, the solution
of the LQ optimal problem will be investigated by considering the Riccati equation
approach. The obtained LQG control will be applied to the Timoshenko beam with
disturbances by providing a stabilizing feedback.