Riccati equations arising in boundary control of fluid structure interactions. (30th May 2007) - Lasiecka, I.; Tuffaha, A.
We consider a boundary control system for a fluid structure interaction model. This system describes the motion of an elastic structure inside a viscous fluid with interaction taking place at the boundary of the structure, and with the possibility of controlling the dynamics from this boundary. Our aim is to construct a real time feedback control based on solution to the Riccati equation. We show that the boundary control problem arising in fluid structure interaction falls in the class of SECS. Once this is accomplished, application of the theory in Lasiecka and Tuffaha (2007) leads to the main result of this paper which is wellposedness of Riccati equations and of Riccati feedback synthesis. In addition to the theoretical results, an explicit formulation of the Differential Riccati equation associated with this control system provides a basis for an effective computational treatment of the system under consideration.