Défense de thèse de doctorat en sciences mathématiques

Analysis and LQG Control of Infinite-dimensional Stochastic Port-Hamiltonian Systems

Membres du jury

• Anne LEMAITRE (UNamur), présidente;
• Joseph WINKIN (UNamur), secrétaire;
• Birgit JACOB (Bergische Universität Wuppertal);
• Yann LE GORREC (Ecole Nationale Supérieure de Mécanique et des Microtechniques, Besançon);
• Alexandre MAUROY (UNamur).
  

Résumé

Stochastic and deterministic port-Hamiltonian systems with both distributed and boundary controls along with distributed and boundary observations are considered in this work. The concept of well-posedness in the sense of Weiss-Salamon is generalized to infinite-dimensional stochastic systems. Under this extended definition, stochastic port-Hamiltonians systems are proved to be well-posed under some assumptions. We then address the LQG control problem for stochastic port-Hamiltonian systems with bounded control, observation and noise operators. We further derive conditions under which the Hamiltonian framework is preserved in the LQG controller dynamics. Throughout this thesis, the theory is illustrated on an example of an inhomogeneous vibrating string subject to some space and time Gaussian white noise process representing environment disturbances. Finally, we propose a new model based on the port-Hamiltonian approach and a control law for a compliant bio-medical endoscope actuated by electro-active polymers.

The thesis defence is open to the public.

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