A spectral approach for the exact observability of infinite dimensional systems with skew-adjoint generator.

By Karim Ramdani, Takéo Takahashi, Gerald Tenenbaum, Marius Tucsnak. 2005

96 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/120573eabf316ab62b65593cc094fc93b2b9add9

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Citations in the corpus

Non-uniform stability for bounded semi-groups on Banach spaces (2008, background): “Such spectral criteria have also proved efficient in control theory [29, 7, 21, 27].”
New blow-up rates for fast controls of Schrödinger and heat equations (2007, background): “It has been recently shown in Ramdani, Takahashi, Tenenbaum and Tucsnak [18] that if Ω is a square in R2 then the system determined by (6.”
Observation and Control for Operator Semigroups (2009, background): “We refer to Ramdani, Takahashi, Tenenbaum and Tucsnak [186] and to [219] for results in this direction.”
A SYSTEMATIC METHOD FOR BUILDING SMOOTH CONTROLS FOR SMOOTH DATA (2010, background): “[11], Carleman estimates [23], [7], non-harmonic Fourier series [9], [18] or pseudodifferential operators [1], [3].”
Resolvent conditions for the control of unitary groups and their approximations (2012, methodology): “This improves on earlier results in [26], [30], and [38] linking first and second order equations, and in [11], [12], and [13] linking infinite-dimensional equations and their finite-dimensional semi-discretization.”
Local controllability of 1D linear and nonlinear Schr (2010, unknown): “For linear equations, the controllability is equivalent to an observability inequality that may be proved with di erent technics: multiplier methods (see [36] by Fabre, [47] by Machtyngier), microlocal analysis (see [46] by Lebeau, [27] by Burq), Carleman estimates (see [42, 43] by Lasiecka, Triggia”
The Wave Equation: Control and Numerics (2012, methodology): “The proof of this statement can be derived using resolvent estimates [16, 79] (see also [88] for a similar estimate) but this method does not yield sharp estimates on the observability time.”
Controllability of the discrete-spectrum Schrödinger equation driven by an external field (2008, background): “Some results are available when the control is the value of the wave function on some portion of the boundary or in some internal region of the domain (see [41] and references therein and the recent paper [39]).”
Sharp polynomial decay rates for the damped wave equation on the torus (2012, methodology): “In particular [Miller 2005, Theorem 5.1] (or [Tucsnak and Weiss 2009, Theorem 6.6.1]) yields that system (2-1) is observable in some time T > 0 if and only if there exists a constant C > 0 such that we have ‖u‖2H ≤ C ( ‖(A− λ Id)u‖2H +‖B ∗u‖2Y ) for all λ ∈ R and u ∈ D(A).”