Control Theory for Partial Differential Equations: Continuous and Approximation Theories

By Irena Lasiecka, Roberto Triggiani. 2000

771 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/1fdfb9dcf7d41b94ad0efdf4d08b84bdc2498263

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

Control theory: history, mathematical achievements and perspectives (2003, background): “For more details, the reader is referred to the books [21] and [27] and the survey papers [13], [54] and [55].”
Semigroups for Delay Equations (2005, background): “Then (1) becomes a feedback system as studied, for example, in Curtain, Zwart [16], Lasiecka, Triggiani [54].”
BDF Methods for Large-Scale Differential Riccati Equations (2004, background): “Imposing a quadratic cost functional, the solution of the optimal control is often given via feedback control where the feedback operator is given in terms of an operator-valued differential Riccati equation, see [28, 23, 24, 25].”
Exact controllability of semilinear plate equations (2001, unknown): “Extensive related references can be found in [1,3–7,9,13 For the semilinear case, the exact boundary controllability problem of system (1.2) with controller Σ 0 = Σ was discussed in [8] for nonlinearity f ( · ) satisfying the following assumptions: f is absolutely continuous and for some constant L…”
A Semigroup Approach to Boundary Feedback Systems (2003, methodology): “, the monographs by Lasiecka–Triggiani [LT00], the papers by Desch et al.”
Anisotropic function spaces and maximal regularity for parabolic problems Part 1: Function spaces (2009, unknown): “Triggiani [46] for more recent developments).”
CONTROLLABILITY OF PARTIAL DIFFERENTIAL EQUATIONS AND ITS SEMI-DISCRETE APPROXIMATIONS (2006, background): “For more details, the reader is referred to the books [126] and [130] and the survey papers [82], [237] and [235].”
Admissibility of Control and Observation Operators for Semigroups: A Survey (2004, result): “For example, authors such as Lions [49], Butkovsky [4], and Lasiecka and Triggiani [45, 46] have very successfully studied systems described by partial differential equations, whereas other authors including Mitter and Delfour [13], Marshall [50], Dym et al.”
Global uniqueness, observability and stabilization of nonconservative Schrödinger equations via pointwise Carleman estimates. Part II: L 2(Ω)-estimates (2004, methodology): “Ñ∗A∗φ = Ñ∗Aφ =  0 on Γ0 −φ on Γ1 φ ∈ D(A) [18].”
Backstepping observers for a class of parabolic PDEs (2005, unknown): “Past efforts in linear observer design for PDEs include the infinite dimensional Luenberger approach [7,11].”
Uniqueness of weak solutions for the semilinear wave equations with supercritical boundary/interior sources and damping (2008, background): “The idea is to exploit the boundary dissipation as a sort of “regularization” [23].”
Characterization by observability inequalities of controllability and stabilization properties (2018, methodology): “Since the critical fact is only in the use of Riccati theory in Lemma 4, there are anyway some particular situations where the semigroup is not analytic, the control operator is admissible, and however Riccati theory is established (see [17]).”