Observation and Control for Operator Semigroups
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1 Birkhäuser Advanced Texts Basler Lehrbücher Observation and Control for Operator Semigroups Bearbeitet von Marius Tucsnak, George Weiss Approx. 496 p Buch. xi, 483 S. Hardcover ISBN Format (B x L): 17 x 24,4 cm Gewicht: 1024 g Weitere Fachgebiete > Mathematik > Mathematische Analysis > Differentialrechnungen und -gleichungen schnell und portofrei erhältlich bei Die Online-Fachbuchhandlung beck-shop.de ist spezialisiert auf Fachbücher, insbesondere Recht, Steuern und Wirtschaft. Im Sortiment finden Sie alle Medien (Bücher, Zeitschriften, CDs, ebooks, etc.) aller Verlage. Ergänzt wird das Programm durch Services wie Neuerscheinungsdienst oder Zusammenstellungen von Büchern zu Sonderpreisen. Der Shop führt mehr als 8 Millionen Produkte.
2 Preface ix 1 Observability and Controllability for Finite-dimensional Systems 1.1 Norms and inner products Operators on finite-dimensional spaces Matrix exponentials Observability and controllability for finite-dimensional linear systems TheHautustestandGramians Operator Semigroups 2.1 Strongly continuous semigroups and their generators The spectrum and the resolvents of an operator The resolvents of a semigroup generator and the space D(A ) Invariant subspaces for semigroups Riesz bases Diagonalizable operators and semigroups Strongly continuous groups The adjoint semigroup The embeddings V H V The spaces X 1 and X Bounded perturbations of a generator Semigroups of Contractions 3.1 Dissipative and m-dissipative operators Self-adjoint operators Positive operators The spaces H Sturm Liouville operators TheDirichletLaplacian Skew-adjoint operators v
3 vi 3.8 The theorems of Lumer Phillips and Stone The wave equation with boundary damping Control and Observation Operators 4.1 Solutions of non-homogeneous equations Admissible control operators Admissible observation operators The duality between the admissibility concepts Two representation theorems Infinite-time admissibility Remarks and bibliographical notes on Chapter Testing Admissibility 5.1 Gramians and Lyapunov inequalities Admissible control operators for left-invertible semigroups Admissibility for diagonal semigroups Some unbounded perturbations of generators Admissible control operators for perturbed semigroups Remarks and bibliographical notes on Chapter Observability 6.1 Some observability concepts Some examples based on the string equation Robustness of exact observability with respect to admissible perturbations of the generator Simultaneous exact observability A Hautus-type necessary condition for exact observability Hautus-type tests for exact observability with a skew-adjoint generator From ẅ = A 0 w to ż = ia 0 z From first- to second-order equations Spectral conditions for exact observability with a skew-adjoint generator The clamped Euler Bernoulli beam with torque observation at an endpoint Remarks and bibliographical notes on Chapter Observation for the Wave Equation 7.1 An admissibility result for boundary observation Boundary exact observability A perturbed wave equation The wave equation with distributed observation Some consequences for the Schrödinger and plate equations
4 vii 7.6 The wave equation with boundary damping and boundary velocityobservation Remarks and bibliographical notes on Chapter Non-harmonic Fourier Series and Exact Observability 8.1 A theorem of Ingham Variable coefficients PDEs in one space dimension with boundary observation Domains associated with a sequence The results of Kahane and Beurling The Schrödinger and plate equations in a rectangular domain with distributed observation Remarks and bibliographical notes on Chapter Observability for Parabolic Equations 9.1 Preliminary results From ẅ = A 0 w to ż = A 0 z Final state observability with geometric conditions A global Carleman estimate for the heat operator Final state observability without geometric conditions Remarks and bibliographical notes on Chapter Boundary Control Systems 10.1 What is a boundary control system? Two simple examples in one space dimension A one-dimensional heat equation with Neumann boundary control A string equation with Neumann boundary control A string equation with variable coefficients An Euler Bernoulli beam with torque control An Euler Bernoulli beam with angular velocity control The Dirichlet map on an n-dimensional domain Heat and Schrödinger equations with boundary control The convection-diffusion equation with boundary control The wave equation with Dirichlet boundary control Remarks and bibliographical notes on Chapter Controllability 11.1 Some controllability concepts The duality between controllability and observability Simultaneous controllability and the reachable space with H 1 inputs Anexampleofacoupledsystem
5 viii 11.5 Null-controllability for heat and convection-diffusion equations Boundary controllability for Schrödinger and wave equations Boundary controllability for the Schrödinger equation Boundary controllability for the wave equation Remarks and bibliographical notes on Chapter Appendix I: Some Background on Functional Analysis 12.1 The closed-graph theorem and some consequences Compact operators The square root of a positive operator The Fourier and Laplace transformations Banach space-valued L p functions Appendix II: Some Background on Sobolev Spaces 13.1 Test functions Distributions on a domain The operators div, grad, rot and Definition and first properties of Sobolev spaces Regularity of the boundary and Sobolev spaces on manifolds Trace operators and the space HΓ 1 0 (Ω) The Green formulas and extensions of trace operators Appendix III: Some Background on Differential Calculus 14.1 Critical points and Sard s theorem Existence of Morse functions on Ω Proof of Theorem Appendix IV: Unique Continuation for Elliptic Operators 15.1 A Carleman estimate for elliptic operators The unique continuation results Bibliography List of Notation Index
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