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 Theory of Stabilization for Linear Boundary Control Systems written by Takao Nambu and published by CRC Press. This book was released on 2017-03-03 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a unified algebraic approach to stabilization problems of linear boundary control systems with no assumption on finite-dimensional approximations to the original systems, such as the existence of the associated Riesz basis. A new proof of the stabilization result for linear systems of finite dimension is also presented, leading to an explicit design of the feedback scheme. The problem of output stabilization is discussed, and some interesting results are developed when the observability or the controllability conditions are not satisfied.
Download or read book Boundary Stabilization of Thin Plates written by John E. Lagnese and published by SIAM. This book was released on 1989-01-01 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents one of the main directions of research in the area of design and analysis of feedback stabilizers for distributed parameter systems in structural dynamics. Important progress has been made in this area, driven, to a large extent, by problems in modern structural engineering that require active feedback control mechanisms to stabilize structures which may possess only very weak natural damping. Much of the progress is due to the development of new methods to analyze the stabilizing effects of specific feedback mechanisms. Boundary Stabilization of Thin Plates provides a comprehensive and unified treatment of asymptotic stability of a thin plate when appropriate stabilizing feedback mechanisms acting through forces and moments are introduced along a part of the edge of the plate. In particular, primary emphasis is placed on the derivation of explicit estimates of the asymptotic decay rate of the energy of the plate that are uniform with respect to the initial energy of the plate, that is, on uniform stabilization results. The method that is systematically employed throughout this book is the use of multipliers as the basis for the derivation of a priori asymptotic estimates on plate energy. It is only in recent years that the power of the multiplier method in the context of boundary stabilization of hyperbolic partial differential equations came to be realized. One of the more surprising applications of the method appears in Chapter 5, where it is used to derive asymptotic decay rates for the energy of the nonlinear von Karman plate, even though the technique is ostensibly a linear one.
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 Boundary Stabilization of Parabolic Equations written by Ionuţ Munteanu and published by Springer. This book was released on 2019-02-15 with total page 222 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 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 Tangential Boundary Stabilization of Navier Stokes Equations written by Viorel Barbu and published by American Mathematical Soc.. This book was released on 2006 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: In order to inject dissipation as to force local exponential stabilization of the steady-state solutions, an Optimal Control Problem (OCP) with a quadratic cost functional over an infinite time-horizon is introduced for the linearized N-S equations. As a result, the same Riccati-based, optimal boundary feedback controller which is obtained in the linearized OCP is then selected and implemented also on the full N-S system. For $d=3$, the OCP falls definitely outside the boundaries of established optimal control theory for parabolic systems with boundary controls, in that the combined index of unboundedness--between the unboundedness of the boundary control operator and the unboundedness of the penalization or observation operator--is strictly larger than $\tfrac{3}{2}$, as expressed in terms of fractional powers of the free-dynamics operator. In contrast, established (and rich) optimal control theory [L-T.2] of boundary control parabolic problems and corresponding algebraic Riccati theory requires a combined index of unboundedness strictly less than 1. An additional preliminary serious difficulty to overcome lies at the outset of the program, in establishing that the present highly non-standard OCP--with the aforementioned high level of unboundedness in control and observation operators and subject, moreover, to the additional constraint that the controllers be pointwise tangential--be non-empty; that is, it satisfies the so-called Finite Cost Condition [L-T.2].
Download or read book Advances in Neural Networks ISNN 2024 written by Xinyi Le and published by Springer Nature. This book was released on with total page 635 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Exact Controllability and Stabilization of the Wave Equation written by Enrique Zuazua and published by Springer Nature. This book was released on with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mechanics and Control written by R.S. Guttalu and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Workshop on Control Mechanics has been held at the University of South ern California annually since 1988 under the leadership of late Professor Janislaw M. Skowronski. The primary goal of Professor Skowronski in organizing this series of work shops was to promote the use of advanced mechanics method in control theory with a special emphasis on the control of nonlinear mechanical systems subject to uncertainty. This goal has been achieved through a consistent participation of a large number of researchers in the field of control and mechanics and an intensive exchange of their ideas. Professor Skowronski passed away unexpectedly on March 21, 1992, after the conclusion of the Fifth Workshop. The great success of the Fifth Workshop as well as the entire Control Mechanics Workshops over the years is almost exclusively due to his dedication, enthusiasm, and organizational capabilities. His untimely demise is a great loss to us and to the mechanics and control community. The proceedings of the Fifth Workshop presented in this volume are dedicated to Professor Angelo Miele, one of the pioneers and ,a leading contributor in many fields of control theory and its applications. His contribution spans a wide range of topics such as optimization theory, flight mechanics, astrodynamics, ocean engineering, and numerical methods. The presentations in the workshop reflected many of the areas in which Professor Miele has been active. The papers included in this volume are divided into three major groups of topics.
Download or read book Boundary Control of PDEs written by Miroslav Krstic and published by SIAM. This book was released on 2008-09-25 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: A clear and concise introduction to backstepping, an elegant new approach to boundary control of partial differential equations (PDEs).
Download or read book Recent Advances in Modeling Analysis and Systems Control Theoretical Aspects and Applications written by El Hassan Zerrik and published by Springer Nature. This book was released on 2019-08-26 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes recent developments in a wide range of areas, including the modeling, analysis and control of dynamical systems, and explores related applications. The book provided a forum where researchers have shared their ideas, results on theory, and experiments in application problems. The current literature devoted to dynamical systems is quite large, and the authors’ choice for the considered topics was motivated by the following considerations. Firstly, the mathematical jargon for systems theory remains quite complex and the authors feel strongly that they have to maintain connections between the people of this research field. Secondly, dynamical systems cover a wider range of applications, including engineering, life sciences and environment. The authors consider that the book is an important contribution to the state of the art in the fuzzy and dynamical systems areas.
Download or read book Applied Mechanics Reviews written by and published by . This book was released on 2005 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Analysis Applications and Computations written by Uwe Kähler and published by Springer Nature. This book was released on 2023-12-01 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the contributions of the participants of the 13th International ISAAC Congress 2021, held in Ghent, Belgium. The papers, written by respected international experts, address recent results in mathematics, with a special focus on analysis. The volume provides to both specialists and non-specialists an excellent source of information on current research in mathematical analysis and its various interdisciplinary applications.
Download or read book Dynamics and Control of Mechanical Systems in Offshore Engineering written by Wei He and published by Springer Science & Business Media. This book was released on 2013-10-02 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dynamics and Control of Mechanical Systems in Offshore Engineering is a comprehensive treatment of marine mechanical systems (MMS) involved in processes of great importance such as oil drilling and mineral recovery. Ranging from nonlinear dynamic modeling and stability analysis of flexible riser systems, through advanced control design for an installation system with a single rigid payload attached by thrusters, to robust adaptive control for mooring systems, it is an authoritative reference on the dynamics and control of MMS. Readers will gain not only a complete picture of MMS at the system level, but also a better understanding of the technical considerations involved and solutions to problems that commonly arise from dealing with them. The text provides: · a complete framework of dynamical analysis and control design for marine mechanical systems; · new results on the dynamical analysis of riser, mooring and installation systems together with a general modeling method for a class of MMS; · a general method and strategy for realizing the control objectives of marine systems with guaranteed stability the effectiveness of which is illustrated by extensive numerical simulation; and · approximation-based control schemes using neural networks for installation of subsea structures with attached thrusters in the presence of time-varying environmental disturbances and parametric uncertainties. Most of the results presented are analytical with repeatable design algorithms with proven closed-loop stability and performance analysis of the proposed controllers is rigorous and detailed. Dynamics and Control of Mechanical Systems in Offshore Engineering is primarily intended for researchers and engineers in the system and control community, but graduate students studying control and marine engineering will also find it a useful resource as will practitioners working on the design, running or maintenance of offshore platforms.
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 Trends in PDE Constrained Optimization written by Günter Leugering and published by Springer. This book was released on 2014-12-22 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization problems subject to constraints governed by partial differential equations (PDEs) are among the most challenging problems in the context of industrial, economical and medical applications. Almost the entire range of problems in this field of research was studied and further explored as part of the Deutsche Forschungsgemeinschaft (DFG) priority program 1253 on “Optimization with Partial Differential Equations” from 2006 to 2013. The investigations were motivated by the fascinating potential applications and challenging mathematical problems that arise in the field of PDE constrained optimization. New analytic and algorithmic paradigms have been developed, implemented and validated in the context of real-world applications. In this special volume, contributions from more than fifteen German universities combine the results of this interdisciplinary program with a focus on applied mathematics. The book is divided into five sections on “Constrained Optimization, Identification and Control”, “Shape and Topology Optimization”, “Adaptivity and Model Reduction”, “Discretization: Concepts and Analysis” and “Applications”. Peer-reviewed research articles present the most recent results in the field of PDE constrained optimization and control problems. Informative survey articles give an overview of topics that set sustainable trends for future research. This makes this special volume interesting not only for mathematicians, but also for engineers and for natural and medical scientists working on processes that can be modeled by PDEs.
