Observation and Control for Operator Semigroups

By Marius Tucsnak, George Weiss. 2009

1,520 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/613f907714747d3e1ad57803fa43835a2ad88ea1

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Citations in the corpus

On continuity of solutions for parabolic control systems and input-to-state stability (2017, background): “However, the question for Hilbert spaces U and X was the starting point of intensive research around what has become known as the Weiss conjecture, see [15,33] for surveys.”
Characterization by observability inequalities of controllability and stabilization properties (2018, background): “, heat, wave, Schrödinger equations), such inequalities are instrumental to establish controllability properties (see the textbooks [8, 17, 20, 30, 33, 34]).”
RECENT RESULTS ON THE CONTROLLABILITY OF LINEAR COUPLED PARABOLIC PROBLEMS: A SURVEY (2011, background): “Item 1 to 5 are well-known and the proofs can be found for instance in [66] and [67].”
Minimal time for the null controllability of parabolic systems: The effect of the condensation index of complex sequences (2014, background): “For a proof of the previous result see for instance [12] or [29].”
Exponential stability of abstract evolution equations with time delay (2014, background): “3 of [15] this is equivalent to the fact that C∗ is an admissible operator for the semigroup S.”
Null controllability for parabolic equations with dynamic boundary conditions of reactive-diffusive type (2013, background): “We refer to [33] for a discussion of various controllability and observability concepts.”
Optimal Shape and Location of Sensors for Parabolic Equations with Random Initial Data (2014, background): “It is well known that, if A0 is the negative of the Dirichlet, or Neumann, or Robin Laplacian, then the Equation (8) is observable (see [18,22,40,61]), for every open subset ω of .”
On the null-controllability of diffusion equations (2011, methodology): “2 that B is an admissible control operator for the semigroup generated by A – see, for instance [11], Section 4.”
New phenomena for the null controllability of parabolic systems: Minimal time and geometrical dependence (2016, background): “For a proof see, for instance, [37], [15], [36] or [21].”
2d Grushin-type equations: Minimal time and null controllable data (2015, methodology): “Using a classical duality argument (see [16, 27] by Dolecki, Russell and Lions for pioneer works and [33] by Tucsnak and Weiss for a complete overview), if (2.”
Well-posedness and regularity of hyperbolic boundary control systems on a one-dimensional spatial domain (2010, background): “Using a result by Weiss [26], we know that this connected case will lead to a well-posed system, provided the feedback gives a bounded closed loop transfer function.”
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).”
Exponential sensitivity and turnpike analysis for linear quadratic optimal control of general evolution equations (2020, background): “in [26] has to be employed to cover the case of boundary control.”
Indirect controllability of locally coupled wave-type systems and applications (2013, neutral): “(L2(Ω))2 × (H−1(Ω))2, in the sense of transposition solution (see [22,31]).”