Control Theory for Partial Differential Equations
Author | : Irena Lasiecka |
Publisher | : |
Total Pages | : |
Release | : 2000 |
Genre | : Control theory |
ISBN | : |
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Author | : Irena Lasiecka |
Publisher | : |
Total Pages | : |
Release | : 2000 |
Genre | : Control theory |
ISBN | : |
Author | : Irena Lasiecka |
Publisher | : |
Total Pages | : |
Release | : 2013-08-13 |
Genre | : |
ISBN | : 9781299749214 |
First of a two-volume treatise on deterministic control systems modeled by multi-dimensional partial differential equations, originally published in 2000.
Author | : Irena Lasiecka |
Publisher | : Cambridge University Press |
Total Pages | : 678 |
Release | : 2000-02-13 |
Genre | : Mathematics |
ISBN | : 9780521434089 |
First of a two-volume treatise on deterministic control systems modeled by multi-dimensional partial differential equations, originally published in 2000.
Author | : Irena Lasiecka |
Publisher | : |
Total Pages | : |
Release | : 2000 |
Genre | : |
ISBN | : 9781139886437 |
Author | : Guenter Leugering |
Publisher | : Chapman and Hall/CRC |
Total Pages | : 416 |
Release | : 2005-05-27 |
Genre | : Mathematics |
ISBN | : 9780824725464 |
The field of control theory in PDEs has broadened considerably as more realistic models have been introduced and investigated. This book presents a broad range of recent developments, new discoveries, and mathematical tools in the field. The authors discuss topics such as elasticity, thermo-elasticity, aero-elasticity, interactions between fluids and elastic structures, and fluid dynamics and the new challenges that they present. Other control theoretic problems include parabolic systems, dynamical Lame systems, linear and nonlinear hyperbolic equations, and pseudo-differential operators on a manifold. This is a valuable tool authored by international specialists in the field.
Author | : Irena Lasiecka |
Publisher | : Cambridge University Press |
Total Pages | : 458 |
Release | : 2000-02-13 |
Genre | : Mathematics |
ISBN | : 9780521584012 |
Second of a two-volume treatise on deterministic control systems modeled by multi-dimensional partial differential equations.
Author | : Irena Lasiecka |
Publisher | : Cambridge University Press |
Total Pages | : 672 |
Release | : 2000-02-13 |
Genre | : Mathematics |
ISBN | : 9780521434089 |
This is the first volume of a comprehensive and up-to-date 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. The authors describe both continuous theory and numerical approximation. They use an abstract space, operator theoretic approach, based on semigroups methods and unifying 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 I includes the abstract parabolic theory (continuous theory and numerical approximation theory) for the finite and infinite cases and corresponding PDE illustrations, and presents numerous new 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.
Author | : Fatiha Alabau-Boussouira |
Publisher | : Springer |
Total Pages | : 276 |
Release | : 2019-07-04 |
Genre | : Mathematics |
ISBN | : 3030179494 |
This book presents cutting-edge contributions in the areas of control theory and partial differential equations. Over the decades, control theory has had deep and fruitful interactions with the theory of partial differential equations (PDEs). Well-known examples are the study of the generalized solutions of Hamilton-Jacobi-Bellman equations arising in deterministic and stochastic optimal control and the development of modern analytical tools to study the controllability of infinite dimensional systems governed by PDEs. In the present volume, leading experts provide an up-to-date overview of the connections between these two vast fields of mathematics. Topics addressed include regularity of the value function associated to finite dimensional control systems, controllability and observability for PDEs, and asymptotic analysis of multiagent systems. The book will be of interest for both researchers and graduate students working in these areas.
Author | : J. F. Pommaret |
Publisher | : Springer Science & Business Media |
Total Pages | : 578 |
Release | : 2001 |
Genre | : Mathematics |
ISBN | : 9780792370352 |
Algebraic analysis, that is the algebraic study of systems of partial differential equations by means of module theory and homological algebra, was pioneered around 1970 by M. Kashiwara, B. Malgrange, and V.P. Palamodov. The theory of differential modules, namely modules over a noncommutative ring of differential operators, is a fashionable subject of research today. However, despite its fundamental importance in mathematics, it can only be found in specialist books and papers, and has only been applied in control theory since 1990. This book provides an account of algebraic analysis and its application to control systems defined by partial differential equations. The first volume presents the mathematical tools needed from both commutative algebra, homological algebra, differential geometry and differential algebra. The second volume applies these new methods in order to study the structural and input/output properties of both linear and nonlinear control systems. Hundreds of explicit examples allow the reader to gain insight and experience in these topics.
Author | : Qi Lü |
Publisher | : Springer Nature |
Total Pages | : 592 |
Release | : 2021-10-19 |
Genre | : Science |
ISBN | : 3030823318 |
This is the first book to systematically present control theory for stochastic distributed parameter systems, a comparatively new branch of mathematical control theory. The new phenomena and difficulties arising in the study of controllability and optimal control problems for this type of system are explained in detail. Interestingly enough, one has to develop new mathematical tools to solve some problems in this field, such as the global Carleman estimate for stochastic partial differential equations and the stochastic transposition method for backward stochastic evolution equations. In a certain sense, the stochastic distributed parameter control system is the most general control system in the context of classical physics. Accordingly, studying this field may also yield valuable insights into quantum control systems. A basic grasp of functional analysis, partial differential equations, and control theory for deterministic systems is the only prerequisite for reading this book.