[CvGmt News] seminario Priola 4/6
Daniele Castorina
castorin at mat.uniroma2.it
Wed May 29 18:09:46 CEST 2013
Cari amici,
vi segnalo il prossimo seminario di ED a Tor Vergata:
Martedi' 4 Giugno 2013, h 14:30, Aula Dal Passo
Enrico Priola - Università di Torino
"Linear Operator Inequality and Null Controllability with Vanishing
Energy for unbounded control systems."
We consider linear systems on a separable Hilbert space $H$, which
are null controllable at some time $T_0>0$ under the action of a
point or boundary control. Parabolic and hyperbolic control systems
usually studied in applications are special cases. To every initial
state $ y_0 \in H$ we associate the minimal "energy" needed to
transfer $ y_0 $ to $ 0 $ in a time $ T \ge T_0$ ("energy" of a
control being the square of its $ L^2 $ norm). We give both
necessary and sufficient conditions under which the minimal energy
converges to $ 0 $ for $ T\to+\infty $. This extends to boundary
control systems the concept of null controllability with vanishing
energy introduced by Priola and Zabczyk (Siam J. Control Optim. 42
(2003)) for distributed systems. The proofs in Priola-Zabczyk paper
depend on properties of the associated Riccati equation, which are
not available in the present, general setting. Here we base our
results on new properties of the quadratic regulator problem with
stability and the Linear Operator Inequality.
--
Daniele Castorina
Dipartimento di Matematica - Studio 1221
Università di Roma "Tor Vergata"
Via della Ricerca Scientifica 00133 Roma
email: castorin at mat.uniroma2.it
tel: +390672594653
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