Controllability and Stabilization of Parabolic Equations, Viorel Barbu
Автор: VIOREL BARBU Название: Controllability and Stabilization of Parabolic Equations ISBN: 3319766651 ISBN-13(EAN): 9783319766652 Издательство: Springer Рейтинг: Цена: 13974.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This monograph presents controllability and stabilization methods in control theory that solve parabolic boundary value problems.
Автор: Ionu? Munteanu Название: Boundary Stabilization of Parabolic Equations ISBN: 3030110982 ISBN-13(EAN): 9783030110987 Издательство: Springer Рейтинг: Цена: 11878.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
This monograph presents a technique, developed by the author, to design asymptotically exponentially stabilizing finite-dimensional boundary proportional-type feedback controllers for nonlinear parabolic-type equations. The potential control applications of this technique are wide ranging in many research areas, such as Newtonian fluid flows modeled by the Navier-Stokes equations; electrically conducted fluid flows; phase separation modeled by the Cahn-Hilliard equations; and deterministic or stochastic semi-linear heat equations arising in biology, chemistry, and population dynamics modeling.
The text provides answers to the following problems, which are of great practical importance:
Designing the feedback law using a minimal set of eigenfunctions of the linear operator obtained from the linearized equation around the target stateDesigning observers for the considered control systemsConstructing time-discrete controllers requiring only partial knowledge of the state
After reviewing standard notations and results in functional analysis, linear algebra, probability theory and PDEs, the author describes his novel stabilization algorithm. He then demonstrates how this abstract model can be applied to stabilization problems involving magnetohydrodynamic equations, stochastic PDEs, nonsteady-states, and more.
Boundary Stabilization of Parabolic Equations will be of particular interest to researchers in control theory and engineers whose work involves systems control. Familiarity with linear algebra, operator theory, functional analysis, partial differential equations, and stochastic partial differential equations is required.
Описание: This book presents a concise study of controllability theory of partial differential equations when they are equipped with actuators and/or sensors that are finite dimensional at every moment of time.
Описание: In a typical mathematical model of a controlled distributed parameter process one usually ?nds either boundary or internal locally distributed controls to serve as the means to describe the effect of external actuators on the process at hand. H- ever, these classical controls, enteringthe modelequationsas additive terms, are not suitable to deal with a vast array of processes that can change their principal intr- sic properties due to the control actions. Important examples here include (but not limitedto)thechainreaction-typeprocessesinbiomedical, nuclear, chemicalan- nancial applications, which can changetheir (reaction)rate when certain "catalysts" are applied, and the so-called "smart materials", which can, for instance, alter their frequency response. The goal of this monograph is to address the issue of global controllability of partial differential equations in the context of multiplicative (or bilinear) c- trols, which enter the model equations as coef?cients. The mathematical models of our interest include the linear and nonlinear parabolic and hyperbolic PDE's, the Schrodi ] nger equation, and coupled hybrid nonlinear distributed parameter systems associated with the swimming phenomenon. Pullman, WA, USA Alexander Khapalov January 2010 vii Preface This monograph developed from the research conducted in 2001-2009 in the area of controllability theory of partial differential equations. The concept of control- bility is a principal component of Control Theory which was brought to life in the 1950's by numerous applications in engineering, and has received the most sign- icant attention both from the engineering and the mathematical communities since then.
Автор: Jerzy Klamka Название: Controllability and Minimum Energy Control ISBN: 3030064557 ISBN-13(EAN): 9783030064556 Издательство: Springer Рейтинг: Цена: 13974.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The book offers a comprehensive overview of controllability problems and minimum energy control for broad classes of dynamical systems, including linear, semilinear and nonlinear systems, which are important for modeling systems in automatic control, electrical engineering, mechanics and informatics. It develops the theory of controllability for both finite and infinite dimensional dynamical systems described by differential state equation, and studies in detail functional analysis and matrix algebra, which provide essential and effective tools for the new solutions of a number of important controllability problems. The theoretical results are illustrated by examples throughout the book. Primarily intended for academic researchers working in mathematical control theory, the self-contained text is easily accessible and particularly interesting for control engineering and applied mathematics graduates.
Описание: This book involves the design and analysis of coordination algorithms on networks, identification of dynamic networks, and estimation on networks with random geometries with implications for networks that support the operation of dynamic systems.
Автор: Klamka Название: Controllability and Minimum Energy Control ISBN: 3319925393 ISBN-13(EAN): 9783319925394 Издательство: Springer Рейтинг: Цена: 13974.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The book offers a comprehensive overview of controllability problems and minimum energy control for broad classes of dynamical systems, including linear, semilinear and nonlinear systems, which are important for modeling systems in automatic control, electrical engineering, mechanics and informatics.
Описание: This book involves the design and analysis of coordination algorithms on networks, identification of dynamic networks, and estimation on networks with random geometries with implications for networks that support the operation of dynamic systems.
Описание: The main aim of this treatise is to apply infinite moment theory to the problem of the controllability of one-dimensional vibrating systems, such as strings and beams, and heating processes. A minimum knowledge of functional analysis and partial differential equations is required for this text.
Автор: Jerzy Klamka Название: Controllability of Dynamical Systems ISBN: 0792308220 ISBN-13(EAN): 9780792308225 Издательство: Springer Рейтинг: Цена: 13275.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book introduces a number of recent advances regarding periodic feedback stabilization for linear and time periodic evolution equations. First, it presents selected connections between linear quadratic optimal control theory and feedback stabilization theory for linear periodic evolution equations.
Описание: This book deals with a systematic study of a dynamical system approach to investigate the symmetrization and stabilization properties of nonnegative solutions of nonlinear elliptic problems in asymptotically symmetric unbounded domains. The usage of infinite dimensional dynamical systems methods for elliptic problems in unbounded domains as well as finite dimensional reduction of their dynamics requires new ideas and tools. To this end, both a trajectory dynamical systems approach and new Liouville type results for the solutions of some class of elliptic equations are used. The work also uses symmetry and monotonicity results for nonnegative solutions in order to characterize an asymptotic profile of solutions and compares a pure elliptic partial differential equations approach and a dynamical systems approach. The new results obtained will be particularly useful for mathematical biologists.
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