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Theory Of Stabilization For Linear Boundary Control Systems
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Book Synopsis Theory of Stabilization for Linear Boundary Control Systems by : Takao Nambu
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 285 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.
Book Synopsis Stabilization of Linear Systems by : Vasile Dragan
Download or read book Stabilization of Linear Systems written by Vasile Dragan and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Boundary Stabilization of Parabolic Equations by : Ionuţ Munteanu
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.
Book Synopsis Nonlinear and Optimal Control Systems by : Thomas L. Vincent
Download or read book Nonlinear and Optimal Control Systems written by Thomas L. Vincent and published by John Wiley & Sons. This book was released on 1997-06-23 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Internal and External Stabilization of Linear Systems with Constraints by : Ali Saberi
Download or read book Internal and External Stabilization of Linear Systems with Constraints written by Ali Saberi and published by Springer Science & Business Media. This book was released on 2012-06-21 with total page 846 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Boundary Control of PDEs by : Miroslav Krstic
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.
Book Synopsis Stability and Stabilization of Infinite Dimensional Systems with Applications by : Zheng-Hua Luo
Download or read book Stability and Stabilization of Infinite Dimensional Systems with Applications written by Zheng-Hua Luo and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Stability and Boundary Stabilization of 1-D Hyperbolic Systems by : Georges Bastin
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.
Book Synopsis Advanced Topics in Control Systems Theory by : Antonio Loría
Download or read book Advanced Topics in Control Systems Theory written by Antonio Loría and published by Springer Science & Business Media. This book was released on 2006-02-09 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Linear Control Theory by : Shankar P. Bhattacharyya
Download or read book Linear Control Theory written by Shankar P. Bhattacharyya and published by CRC Press. This book was released on 2018-10-03 with total page 924 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Sensitivity of Automatic Control Systems by : Efim Rozenwasser
Download or read book Sensitivity of Automatic Control Systems written by Efim Rozenwasser and published by CRC Press. This book was released on 2019-04-30 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although it arose much earlier in a variety of contexts, sensitivity theory became an independent branch of science in the sixties. Since then, researchers from around the world have continued to make great strides in both the theory and its applications. However, much of the work of Russian scientific schools and specialists remain unknown in the West. Sensitivity of Control Systems summarizes the results of the authors and their disciples in sensitivity theory, addressing the basic notions of the theory and the problem of selecting technical parameters of systems. The authors formulate problems for actual technical systems and their models, and establish relations between sensitivity theory and classical stability problems. They offer a significant, general theory for investigating the sensitivity of boundary problems and use elements of this theory for sensitivity analysis of solutions to nonlinear programming and variational calculus problems, as well as oscillatory processes. The book also presents general investigation methods for discontinuous systems, including those described by operator models. Full of powerful new methods and results, this book offers a unique opportunity for those in theoretical investigation and in the design, testing, and exploitation of various control systems to explore the work of Russia's leading researchers in sensitivity theory. Furthermore, its techniques for parametric perturbation investigation, Sensitivity of Control Systems will prove useful in fields outside of control theory, including oscillation theory, motion dynamics, and mathematical economy.
Book Synopsis Tangential Boundary Stabilization of Navier-Stokes Equations by : Viorel Barbu
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].
Book Synopsis State Functions and Linear Control Systems by : Donald G. Schultz
Download or read book State Functions and Linear Control Systems written by Donald G. Schultz and published by . This book was released on 1967 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Feedback Control Theory by : John C. Doyle
Download or read book Feedback Control Theory written by John C. Doyle and published by Courier Corporation. This book was released on 2013-04-09 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: An excellent introduction to feedback control system design, this book offers a theoretical approach that captures the essential issues and can be applied to a wide range of practical problems. Its explorations of recent developments in the field emphasize the relationship of new procedures to classical control theory, with a focus on single input and output systems that keeps concepts accessible to students with limited backgrounds. The text is geared toward a single-semester senior course or a graduate-level class for students of electrical engineering. The opening chapters constitute a basic treatment of feedback design. Topics include a detailed formulation of the control design program, the fundamental issue of performance/stability robustness tradeoff, and the graphical design technique of loopshaping. Subsequent chapters extend the discussion of the loopshaping technique and connect it with notions of optimality. Concluding chapters examine controller design via optimization, offering a mathematical approach that is useful for multivariable systems.
Book Synopsis Mathematical Theory of Control Systems Design by : V.N. Afanasiev
Download or read book Mathematical Theory of Control Systems Design written by V.N. Afanasiev and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt: Give, and it shall be given unto you. ST. LUKE, VI, 38. The book is based on several courses of lectures on control theory and appli cations which were delivered by the authors for a number of years at Moscow Electronics and Mathematics University. The book, originally written in Rus sian, was first published by Vysshaya Shkola (Higher School) Publishing House in Moscow in 1989. In preparing a new edition of the book we planned to make only minor changes in the text. However, we soon realized that we like many scholars working in control theory had learned many new things and had had many new insights into control theory and its applications since the book was first published. Therefore, we rewrote the book especially for the English edition. So, this is substantially a new book with many new topics. The book consists of an introduction and four parts. Part One deals with the fundamentals of modern stability theory: general results concerning stability and instability, sufficient conditions for the stability of linear systems, methods for determining the stability or instability of systems of various type, theorems on stability under random disturbances.
Book Synopsis Modern Control System Theory by : M. Gopal
Download or read book Modern Control System Theory written by M. Gopal and published by New Age International. This book was released on 1993 with total page 712 pages. Available in PDF, EPUB and Kindle. Book excerpt: About the book... The book provides an integrated treatment of continuous-time and discrete-time systems for two courses at postgraduate level, or one course at undergraduate and one course at postgraduate level. It covers mainly two areas of modern control theory, namely; system theory, and multivariable and optimal control. The coverage of the former is quite exhaustive while that of latter is adequate with significant provision of the necessary topics that enables a research student to comprehend various technical papers. The stress is on interdisciplinary nature of the subject. Practical control problems from various engineering disciplines have been drawn to illustrate the potential concepts. Most of the theoretical results have been presented in a manner suitable for digital computer programming along with the necessary algorithms for numerical computations.
Book Synopsis Optimization Theory and the Design of Feedback Control Systems by : Charles Wolcott Merriam
Download or read book Optimization Theory and the Design of Feedback Control Systems written by Charles Wolcott Merriam and published by . This book was released on 1964 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt:
