Control Theory for Partial Differential Equations

Volume 2, Abstract Hyperbolic-Like Systems Over a Finite Time Horizon: Continuous and Approximation
Erscheinungsjahr 2010
ISBN: 978-0-521-15568-7
Verlag: Cambridge University Press

Buch, Englisch, Band 75, 454 Seiten, Format (B × H): 156 mm x 234 mm, Gewicht: 685 g

Reihe: Encyclopedia of Mathematics and its Applications

• In-depth, comprehensive coverage
• Wealth of illustrative examples
• Continuous theory and numerical approximation theory

Originally published in 2000, this is the second volume of a comprehensive two-volume treatment of quadratic optimal control theory for partial differential equations over a finite or infinite time horizon, and related differential (integral) and algebraic Riccati equations. Both continuous theory and numerical approximation theory are included. The authors use an abstract space, operator theoretic approach, which is based on semigroups methods, and which unifies across a few basic classes of evolution. The various abstract frameworks are motivated by, and ultimately directed to, partial differential equations with boundary/point control. Volume 2 is focused on the optimal control problem over a finite time interval for hyperbolic dynamical systems. A few abstract models are considered, each motivated by a particular canonical hyperbolic dynamics. It presents numerous fascinating results. These volumes will appeal to graduate students and researchers in pure and applied mathematics and theoretical engineering with an interest in optimal control problems.

Autoren/Hrsg.

Lasiecka, Irena

Triggiani, Roberto

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

1. Categories
2. Categories and exact sequences
3. Change of rings
4. The Morita theory
5. Limits in categories
6. Localization
7. Local-global methods.