[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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