Control Theory for Partial Differential Equations: Volume 2, Abstract Hyperbolic-like Systems over a Finite Time Horizon
Continuous and Approximation Theories

Second of a two-volume treatise on deterministic control systems modeled by multi-dimensional partial differential equations.

Irena Lasiecka (Author), Roberto Triggiani (Author)

9780521155687, Cambridge University Press

Paperback, published 14 April 2011

454 pages
23.4 x 15.6 x 2.3 cm, 0.63 kg

Review of the hardback: 'The reader will find much important information on various aspects of semigroup theory and on the regularity of solutions of hyperbolic equations.' EMS Newsletter

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.

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.

Subject Areas: Differential calculus & equations [PBKJ]