Download or read book Control and Stabilization of Partial Differential Equations written by Kais Ammari and published by SMF. This book was released on 2015-07-01 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Boundary Control of PDEs written by Miroslav Krstic and published by SIAM. This book was released on 2008-01-01 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: The text's broad coverage includes parabolic PDEs; hyperbolic PDEs of first and second order; fluid, thermal, and structural systems; delay systems; PDEs with third and fourth derivatives in space (including variants of linearized Ginzburg-Landau, Schrodinger, Kuramoto-Sivashinsky, KdV, beam, and Navier-Stokes equations); real-valued as well as complex-valued PDEs; stabilization as well as motion planning and trajectory tracking for PDEs; and elements of adaptive control for PDEs and control of nonlinear PDEs.
Download or read book Input to State Stability for PDEs written by Iasson Karafyllis and published by Springer. This book was released on 2018-06-07 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book lays the foundation for the study of input-to-state stability (ISS) of partial differential equations (PDEs) predominantly of two classes—parabolic and hyperbolic. This foundation consists of new PDE-specific tools. In addition to developing ISS theorems, equipped with gain estimates with respect to external disturbances, the authors develop small-gain stability theorems for systems involving PDEs. A variety of system combinations are considered: PDEs (of either class) with static maps; PDEs (again, of either class) with ODEs; PDEs of the same class (parabolic with parabolic and hyperbolic with hyperbolic); and feedback loops of PDEs of different classes (parabolic with hyperbolic). In addition to stability results (including ISS), the text develops existence and uniqueness theory for all systems that are considered. Many of these results answer for the first time the existence and uniqueness problems for many problems that have dominated the PDE control literature of the last two decades, including—for PDEs that include non-local terms—backstepping control designs which result in non-local boundary conditions. Input-to-State Stability for PDEs will interest applied mathematicians and control specialists researching PDEs either as graduate students or full-time academics. It also contains a large number of applications that are at the core of many scientific disciplines and so will be of importance for researchers in physics, engineering, biology, social systems and others.
Download or read book Adaptive Control of Parabolic PDEs written by Andrey Smyshlyaev and published by Princeton University Press. This book was released on 2010-07-01 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Stabilization Optimal and Robust Control written by Aziz Belmiloudi and published by Springer Science & Business Media. This book was released on 2008-08-17 with total page 509 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stabilization, Optimal and Robust Control develops robust control of infinite-dimensional dynamical systems derived from time-dependent coupled PDEs associated with boundary-value problems. Rigorous analysis takes into account nonlinear system dynamics, evolutionary and coupled PDE behaviour and the selection of function spaces in terms of solvability and model quality. Mathematical foundations are provided so that the book remains accessible to the non-control-specialist. Following chapters giving a general view of convex analysis and optimization and robust and optimal control, problems arising in fluid mechanical, biological and materials scientific systems are laid out in detail. The combination of mathematical fundamentals with application of current interest will make this book of much interest to researchers and graduate students looking at complex problems in mathematics, physics and biology as well as to control theorists.
Download or read book Boundary Stabilization of Parabolic Equations written by Ionuţ Munteanu and published by Springer. This book was released on 2019-02-15 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Stabilization of Elastic Systems by Collocated Feedback written by Kaïs Ammari and published by Springer. This book was released on 2014-11-03 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: By introducing a new stabilization methodology, this book characterizes the stability of a certain class of systems. The stability (exponential, polynomial, or weaker) for the closed loop problem is reduced to an observability estimate for the corresponding uncontrolled system combined with a boundedness property of the transfer function of the associated open loop system. A similar strategy is applied to systems where a delay term is added. The book concludes with many concrete examples. This book is addressed to graduate students in mathematics or engineering and also to researchers with an interest in stabilization and control systems governed by partial differential equations.
Download or read book Stabilization of Partial Differential Equations by Finite Dimensional Boundary Feedback Control written by M. Pedersen and published by . This book was released on 1987 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Solvability Regularity and Optimal Control of Boundary Value Problems for PDEs written by Pierluigi Colli and published by Springer. This book was released on 2017-11-03 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume gathers contributions in the field of partial differential equations, with a focus on mathematical models in phase transitions, complex fluids and thermomechanics. These contributions are dedicated to Professor Gianni Gilardi on the occasion of his 70th birthday. It particularly develops the following thematic areas: nonlinear dynamic and stationary equations; well-posedness of initial and boundary value problems for systems of PDEs; regularity properties for the solutions; optimal control problems and optimality conditions; feedback stabilization and stability results. Most of the articles are presented in a self-contained manner, and describe new achievements and/or the state of the art in their line of research, providing interested readers with an overview of recent advances and future research directions in PDEs.
Download or read book Control Of Partial Differential Equations written by Jean-michel Coron and published by World Scientific. This book was released on 2023-04-11 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is mainly a collection of lecture notes for the 2021 LIASFMA International Graduate School on Applied Mathematics. It provides the readers some important results on the theory, the methods, and the application in the field of 'Control of Partial Differential Equations'. It is useful for researchers and graduate students in mathematics or control theory, and for mathematicians or engineers with an interest in control systems governed by partial differential equations.
Download or read book Elementary Feedback Stabilization of the Linear Reaction Convection Diffusion Equation and the Wave Equation written by Weijiu Liu and published by Springer Science & Business Media. This book was released on 2009-12-01 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unlike abstract approaches to advanced control theory, this volume presents key concepts through concrete examples. Once the basic fundamentals are established, readers can apply them to solve other control problems of partial differential equations.
Download or read book Partial Stability and Control written by V.I. Vorotnikov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unlike the conventional research for the general theory of stability, this mono graph deals with problems on stability and stabilization of dynamic systems with respect not to all but just to a given part of the variables characterizing these systems. Such problems are often referred to as the problems of partial stability (stabilization). They naturally arise in applications either from the requirement of proper performance of a system or in assessing system capa bility. In addition, a lot of actual (or desired) phenomena can be formulated in terms of these problems and be analyzed with these problems taken as the basis. The following multiaspect phenomena and problems can be indicated: • "Lotka-Volterra ecological principle of extinction;" • focusing and acceleration of particles in electromagnetic fields; • "drift" of the gyroscope axis; • stabilization of a spacecraft by specially arranged relative motion of rotors connected to it. Also very effective is the approach to the problem of stability (stabilization) with respect to all the variables based on preliminary analysis of partial sta bility (stabilization). A. M. Lyapunov, the founder of the modern theory of stability, was the first to formulate the problem of partial stability. Later, works by V. V. Rumyan tsev drew the attention of many mathematicians and mechanicians around the world to this problem, which resulted in its being intensively worked out. The method of Lyapunov functions became the key investigative method which turned out to be very effective in analyzing both theoretic and applied problems.
Download or read book Optimization and Control for Partial Differential Equations written by Roland Herzog and published by Walter de Gruyter GmbH & Co KG. This book was released on 2022-03-07 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book highlights new developments in the wide and growing field of partial differential equations (PDE)-constrained optimization. Optimization problems where the dynamics evolve according to a system of PDEs arise in science, engineering, and economic applications and they can take the form of inverse problems, optimal control problems or optimal design problems. This book covers new theoretical, computational as well as implementation aspects for PDE-constrained optimization problems under uncertainty, in shape optimization, and in feedback control, and it illustrates the new developments on representative problems from a variety of applications.
Download or read book Stability and Boundary Stabilization of 1 D Hyperbolic Systems written by Georges Bastin and published by Birkhäuser. This book was released on 2016-07-26 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph explores the modeling of conservation and balance laws of one-dimensional hyperbolic systems using partial differential equations. It presents typical examples of hyperbolic systems for a wide range of physical engineering applications, allowing readers to understand the concepts in whichever setting is most familiar to them. With these examples, it also illustrates how control boundary conditions may be defined for the most commonly used control devices. The authors begin with the simple case of systems of two linear conservation laws and then consider the stability of systems under more general boundary conditions that may be differential, nonlinear, or switching. They then extend their discussion to the case of nonlinear conservation laws and demonstrate the use of Lyapunov functions in this type of analysis. Systems of balance laws are considered next, starting with the linear variety before they move on to more general cases of nonlinear ones. They go on to show how the problem of boundary stabilization of systems of two balance laws by both full-state and dynamic output feedback in observer-controller form is solved by using a “backstepping” method, in which the gains of the feedback laws are solutions of an associated system of linear hyperbolic PDEs. The final chapter presents a case study on the control of navigable rivers to emphasize the main technological features that may occur in real live applications of boundary feedback control. Stability and Boundary Stabilization of 1-D Hyperbolic Systems will be of interest to graduate students and researchers in applied mathematics and control engineering. The wide range of applications it discusses will help it to have as broad an appeal within these groups as possible.
Download or read book Optimal Control of Partial Differential Equations written by Karl-Heinz Hoffmann and published by Springer Science & Business Media. This book was released on 1999 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Well-posedness of Semilinear Heat Equations with Iterated Logarithms.- Uniform Stability of Nonlinear Thermoelastic Plates with Free Boundary Conditions.- Exponential Bases in Sobolev Spaces in Control and Observation Problems.- Sampling and Interpolation of Functions with Multi-Band Spectra and Controllability Problems.- Discretization of the Controllability Grammian in View of Exact Boundary Control: the Case of Thin Plates.- Stability of Holomorphic Semigroup Systems under Nonlinear Boundary Perturbations.- Shape Control in Hyperbolic Problems.- Second Order Optimality Conditions for Some Control Problems of Semilinear Elliptic Equations with Integral State Constraints.- Intrinsic P(2, 1) Thin Shell Models and Naghdi's Models without A Priori Assumption on the Stress Tensor.- On the Approximate Controllability for some Explosive Parabolic Problems.- Fréchet-Differentiability and Sufficient Optimality Conditions for Shape Functionals.- State Constrained Optimal Control for some Quasilinear Parabolic Equations.- Controllability property for the Navier-Stokes equations.- Shape Sensitivity and Large Deformation of the Domain for Norton-Hoff Flows.- On a Distributed Control Law with an Application to the Control of Unsteady Flow around a Cylinder.- Homogenization of a Model Describing Vibration of Nonlinear Thin Plates Excited by Piezopatches.- Stabilization of the Dynamic System of Elasticity by Nonlinear Boundary Feedback.- Griffith Formula and Rice-Cherepanov's Integral for Elliptic Equations with Unilateral Conditions in Nonsmooth Domains.- A Domain Optimization Problem for a Nonlinear Thermoelastic System.- Approximate Controllability for a Hydro-Elastic Model in a Rectangular Domain.- Noncooperative Games with Elliptic Systems.- Incomplete Indefinite Decompositions as Multigrid Smoothers for KKT Systems.- Domain Optimization for the Navier-Stokes Equations by an Embedding Domain Method.- On the Approximation and Optimization of Fourth Order Elliptic Systems.- On the Existence and Approximation of Solutions for the Optimal Control of Nonlinear Hyperbolic Conservation Laws.- Identification of Memory Kernels in Heat Conduction and Viscoelasticity.- Variational Formulation for Incompressible Euler Equation by Weak Shape Evolution.
Download or read book Optimal Boundary Control and Boundary Stabilization of Hyperbolic Systems written by Martin Gugat and published by Birkhäuser. This book was released on 2015-07-15 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt: This brief considers recent results on optimal control and stabilization of systems governed by hyperbolic partial differential equations, specifically those in which the control action takes place at the boundary. The wave equation is used as a typical example of a linear system, through which the author explores initial boundary value problems, concepts of exact controllability, optimal exact control, and boundary stabilization. Nonlinear systems are also covered, with the Korteweg-de Vries and Burgers Equations serving as standard examples. To keep the presentation as accessible as possible, the author uses the case of a system with a state that is defined on a finite space interval, so that there are only two boundary points where the system can be controlled. Graduate and post-graduate students as well as researchers in the field will find this to be an accessible introduction to problems of optimal control and stabilization.
Download or read book Mat report written by and published by . This book was released on 1987 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
