Theory Of Stabilization For Linear Boundary Control Systems
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| Author | : Takao Nambu |
| Publisher | : CRC Press |
| Total Pages | : 285 |
| Release | : 2017-03-03 |
| Genre | : Mathematics |
| ISBN | : 1498758487 |
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.
| Author | : Vasile Dragan |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 320 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 1461215706 |
One of the main problems in control theory is the stabilization problem consisting of finding a feedback control law ensuring stability; when the linear approximation is considered, the nat ural problem is stabilization of a linear system by linear state feedback or by using a linear dynamic controller. This prob lem was intensively studied during the last decades and many important results have been obtained. The present monograph is based mainly on results obtained by the authors. It focuses on stabilization of systems with slow and fast motions, on stabilization procedures that use only poor information about the system (high-gain stabilization and adaptive stabilization), and also on discrete time implementa tion of the stabilizing procedures. These topics are important in many applications of stabilization theory. We hope that this monograph may illustrate the way in which mathematical theories do influence advanced technol ogy. This book is not intended to be a text book nor a guide for control-designers. In engineering practice, control-design is a very complex task in which stability is only one of the re quirements and many aspects and facets of the problem have to be taken into consideration. Even if we restrict ourselves to stabilization, the book does not provide just recipes, but it fo cuses more on the ideas lying behind the recipes. In short, this is not a book on control, but on some mathematics of control.
| Author | : Ionuţ Munteanu |
| Publisher | : Springer |
| Total Pages | : 214 |
| Release | : 2019-02-15 |
| Genre | : Science |
| ISBN | : 3030110990 |
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.
| Author | : Thomas L. Vincent |
| Publisher | : John Wiley & Sons |
| Total Pages | : 584 |
| Release | : 1997-06-23 |
| Genre | : Science |
| ISBN | : 9780471042358 |
Designed for one-semester introductory senior-or graduate-level course, the authors provide the student with an introduction of analysis techniques used in the design of nonlinear and optimal feedback control systems. There is special emphasis on the fundamental topics of stability, controllability, and optimality, and on the corresponding geometry associated with these topics. Each chapter contains several examples and a variety of exercises.
| Author | : Ali Saberi |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 846 |
| Release | : 2012-06-21 |
| Genre | : Science |
| ISBN | : 0817647872 |
Unifying two decades of research, this book is the first to establish a comprehensive foundation for a systematic analysis and design of linear systems with general state and input constraints. For such systems, which can be used as models for most nonlinear systems, the issues of stability, controller design, additonal constraints, and satisfactory performance are addressed. The book is an excellent reference for practicing engineers, graduate students, and researchers in control systems theory and design. It may also serve as an advanced graduate text for a course or a seminar in nonlinear control systems theory and design in applied mathematics or engineering departments. Minimal prerequisites include a first graduate course in state-space methods as well as a first course in control systems design.
| Author | : Miroslav Krstic |
| Publisher | : SIAM |
| Total Pages | : 197 |
| Release | : 2008-01-01 |
| Genre | : Mathematics |
| ISBN | : 0898718600 |
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.
| Author | : Zheng-Hua Luo |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 412 |
| Release | : 2012-12-06 |
| Genre | : Computers |
| ISBN | : 1447104196 |
This book reports on recent achievements in stability and feedback stabilization of infinite systems. In particular emphasis is placed on second order partial differential equations, such as Euler-Bernoulli beam equations, which arise from vibration control of flexible robots arms and large space structures. Various control methods such as sensor feedback control and dynamic boundary control are applied to stabilize the equations. Many new theorems and methods are included in the book. Proof procedures of existing theorems are simplified, and detailed proofs have been given to most theorems. New results on semigroups and their stability are presented, and readers can learn several useful techniques for solving practical engineering problems. Until now, the recently obtained research results included in this book were unavailable in one volume. This self-contained book is an invaluable source of information for all those who are familiar with some basic theorems of functional analysis.
| Author | : Georges Bastin |
| Publisher | : Birkhäuser |
| Total Pages | : 317 |
| Release | : 2016-07-26 |
| Genre | : Mathematics |
| ISBN | : 3319320629 |
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.
| Author | : Antonio Loría |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 312 |
| Release | : 2006-02-09 |
| Genre | : Language Arts & Disciplines |
| ISBN | : 9781846283130 |
This book includes selected contributions by lecturers at the third annual Formation d’Automatique de Paris. It provides a well-integrated synthesis of the latest thinking in nonlinear optimal control, observer design, stability analysis and structural properties of linear systems, without the need for an exhaustive literature review. The internationally known contributors to this volume represent many of the most reputable control centers in Europe.
| Author | : Shankar P. Bhattacharyya |
| Publisher | : CRC Press |
| Total Pages | : 924 |
| Release | : 2018-10-03 |
| Genre | : Technology & Engineering |
| ISBN | : 1420019619 |
Successfully classroom-tested at the graduate level, Linear Control Theory: Structure, Robustness, and Optimization covers three major areas of control engineering (PID control, robust control, and optimal control). It provides balanced coverage of elegant mathematical theory and useful engineering-oriented results. The first part of the book develops results relating to the design of PID and first-order controllers for continuous and discrete-time linear systems with possible delays. The second section deals with the robust stability and performance of systems under parametric and unstructured uncertainty. This section describes several elegant and sharp results, such as Kharitonov’s theorem and its extensions, the edge theorem, and the mapping theorem. Focusing on the optimal control of linear systems, the third part discusses the standard theories of the linear quadratic regulator, Hinfinity and l1 optimal control, and associated results. Written by recognized leaders in the field, this book explains how control theory can be applied to the design of real-world systems. It shows that the techniques of three term controllers, along with the results on robust and optimal control, are invaluable to developing and solving research problems in many areas of engineering.
