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Optimal feedback synthesis for Bolza control problem arising in linearized fluid structure interaction. (English) Zbl 1206.35054

Kunisch, Karl (ed.) et al., Optimal control of coupled systems of partial differential equations. Based on the international conference, Oberwolfach, Germany, March 2–8, 2008. Basel: Birkhäuser (ISBN 978-3-7643-8922-2/hbk; 978-3-7643-8923-9/ebook). ISNM. International Series of Numerical Mathematics 158, 171-190 (2009).
The Bolza boundary control problem defined for a linearized fluid structure interaction model is considered. The aim of the work is to show that the control system under consideration falls into the class of singular estimate control systems for which a satisfactory Riccati theory is available. In particular, it is shown that the system satisfies a singular estimate condition, and the conditions laid out in previous research allow for an application of the results on existence, regularity of optimal control and, most importantly, feedback characterization of the control via solutions to a Riccati equation. The optimal control along with the feedback gain operator, while well defined and bounded for transient times, become singular at the terminal time. The singularity is quantified by an algebraic blow up rate.
For the entire collection see [Zbl 1182.49002].

MSC:

35B45 A priori estimates in context of PDEs
35Q35 PDEs in connection with fluid mechanics
35Q93 PDEs in connection with control and optimization
93B52 Feedback control
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