Abstract hyperbolic-like systems over a finite time horizon
著者
書誌事項
Abstract hyperbolic-like systems over a finite time horizon
（Encyclopedia of mathematics and its applications / edited by G.-C. Rota, v. 75 . Control theory for partial differential equations : continuous and approximation theories / Irena Lasiecka,
Cambridge University Press, 2000
- : hardback
- : pbk
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注記
Includes bibliographical references
内容説明・目次
内容説明
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.
目次
- 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.
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