Controllability and Stabilization of Parabolic Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Controllability and Stabilization of Parabolic Equations write by Viorel Barbu. This book was released on 2018-04-26. Controllability and Stabilization of Parabolic Equations available in PDF, EPUB and Kindle. This monograph presents controllability and stabilization methods in control theory that solve parabolic boundary value problems. Starting from foundational questions on Carleman inequalities for linear parabolic equations, the author addresses the controllability of parabolic equations on a variety of domains and the spectral decomposition technique for representing them. This method is, in fact, designed for use in a wider class of parabolic systems that include the heat and diffusion equations. Later chapters develop another process that employs stabilizing feedback controllers with a finite number of unstable modes, with special attention given to its use in the boundary stabilization of Navier–Stokes equations for the motion of viscous fluid. In turn, these applied methods are used to explore related topics like the exact controllability of stochastic parabolic equations with linear multiplicative noise. Intended for graduate students and researchers working on control problems involving nonlinear differential equations, Controllability and Stabilization of Parabolic Equations is the distillation of years of lectures and research. With a minimum of preliminaries, the book leaps into its applications for control theory with both concrete examples and accessible solutions to problems in stabilization and controllability that are still areas of current research.
Boundary Stabilization of Parabolic Equations
Boundary Stabilization of Parabolic Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Boundary Stabilization of Parabolic Equations write by Ionuţ Munteanu. This book was released on 2019-02-15. Boundary Stabilization of Parabolic Equations available in PDF, EPUB and Kindle. 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 state Designing observers for the considered control systems Constructing 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.
Control and Stabilization of Partial Differential Equations
Control and Stabilization of Partial Differential Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Control and Stabilization of Partial Differential Equations write by Kais Ammari. This book was released on 2015-07-01. Control and Stabilization of Partial Differential Equations available in PDF, EPUB and Kindle.
Adaptive Control of Parabolic PDEs
Adaptive Control of Parabolic PDEs - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Adaptive Control of Parabolic PDEs write by Andrey Smyshlyaev. This book was released on 2010-07-01. Adaptive Control of Parabolic PDEs available in PDF, EPUB and Kindle. This book introduces a comprehensive methodology for adaptive control design of parabolic partial differential equations with unknown functional parameters, including reaction-convection-diffusion systems ubiquitous in chemical, thermal, biomedical, aerospace, and energy systems. Andrey Smyshlyaev and Miroslav Krstic develop explicit feedback laws that do not require real-time solution of Riccati or other algebraic operator-valued equations. The book emphasizes stabilization by boundary control and using boundary sensing for unstable PDE systems with an infinite relative degree. The book also presents a rich collection of methods for system identification of PDEs, methods that employ Lyapunov, passivity, observer-based, swapping-based, gradient, and least-squares tools and parameterizations, among others. Including a wealth of stimulating ideas and providing the mathematical and control-systems background needed to follow the designs and proofs, the book will be of great use to students and researchers in mathematics, engineering, and physics. It also makes a valuable supplemental text for graduate courses on distributed parameter systems and adaptive control.
Evolution Equations
Evolution Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Evolution Equations write by Kaïs Ammari. This book was released on 2017-10-05. Evolution Equations available in PDF, EPUB and Kindle. The proceedings of the summer school held at the Université Savoie Mont Blanc, France, 'Mathematics in Savoie 2015', whose theme was long time behavior and control of evolution equations. The event was attended by world-leading researchers from the community of control theory, as well as young researchers from around the globe. This volume contains surveys of active research topics, along with original research papers containing exciting new results on the behavior of evolution equations. It will therefore benefit both graduate students and researchers. Key topics include the recent view on the controllability of parabolic systems that permits the reader to overview the moment method for parabolic equations, as well as numerical stabilization and control of partial differential equations.
