Download or read book Optimal Control Theory for Infinite Dimensional Systems written by Xungjing Li and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: Infinite dimensional systems can be used to describe many phenomena in the real world. As is well known, heat conduction, properties of elastic plastic material, fluid dynamics, diffusion-reaction processes, etc., all lie within this area. The object that we are studying (temperature, displace ment, concentration, velocity, etc.) is usually referred to as the state. We are interested in the case where the state satisfies proper differential equa tions that are derived from certain physical laws, such as Newton's law, Fourier's law etc. The space in which the state exists is called the state space, and the equation that the state satisfies is called the state equation. By an infinite dimensional system we mean one whose corresponding state space is infinite dimensional. In particular, we are interested in the case where the state equation is one of the following types: partial differential equation, functional differential equation, integro-differential equation, or abstract evolution equation. The case in which the state equation is being a stochastic differential equation is also an infinite dimensional problem, but we will not discuss such a case in this book.

Download or read book Infinite Dimensional Systems written by F. Kappel and published by Springer. This book was released on 2006-11-14 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book An Introduction to Infinite Dimensional Linear Systems Theory written by Ruth F. Curtain and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 714 pages. Available in PDF, EPUB and Kindle. Book excerpt: Infinite dimensional systems is now an established area of research. Given the recent trend in systems theory and in applications towards a synthesis of time- and frequency-domain methods, there is a need for an introductory text which treats both state-space and frequency-domain aspects in an integrated fashion. The authors' primary aim is to write an introductory textbook for a course on infinite dimensional linear systems. An important consideration by the authors is that their book should be accessible to graduate engineers and mathematicians with a minimal background in functional analysis. Consequently, all the mathematical background is summarized in an extensive appendix. For the majority of students, this would be their only acquaintance with infinite dimensional systems.

Download or read book Introduction to Infinite Dimensional Systems Theory written by Ruth Curtain and published by Springer Nature. This book was released on 2020-04-05 with total page 759 pages. Available in PDF, EPUB and Kindle. Book excerpt: Infinite-dimensional systems is a well established area of research with an ever increasing number of applications. Given this trend, there is a need for an introductory text treating system and control theory for this class of systems in detail. This textbook is suitable for courses focusing on the various aspects of infinite-dimensional state space theory. This book is made accessible for mathematicians and post-graduate engineers with a minimal background in infinite-dimensional system theory. To this end, all the system theoretic concepts introduced throughout the text are illustrated by the same types of examples, namely, diffusion equations, wave and beam equations, delay equations and the new class of platoon-type systems. Other commonly met distributed and delay systems can be found in the exercise sections. Every chapter ends with such a section, containing about 30 exercises testing the theoretical concepts as well. An extensive account of the mathematical background assumed is contained in the appendix.

Download or read book Chandrasekhar Equations for Infinite Dimensional Systems Part 2 Unbounded Input and Output Case written by and published by . This book was released on 1987 with total page 58 pages. Available in PDF, EPUB and Kindle. Book excerpt: A set of equations known as Chandrasekhar equations arising in the linear quadratic optimal control problem is considered. This paper considers the linear time invariant system defined in Hilbert spaces involving unbounded input and output operators. For a general class of such systems, the Chandrasekhar equations are derived and establish the existence, uniqueness, and regularity results of their solutions established. Keywords: Chandrasekhar equations; Unbounded operators; Boundary control problems.

Download or read book Infinite Dimensional Optimization and Control Theory written by Hector O. Fattorini and published by Cambridge University Press. This book was released on 1999-03-28 with total page 828 pages. Available in PDF, EPUB and Kindle. Book excerpt: Treats optimal problems for systems described by ODEs and PDEs, using an approach that unifies finite and infinite dimensional nonlinear programming.

Download or read book Control Theory of Infinite Dimensional Systems written by Joachim Kerner and published by Springer Nature. This book was released on 2020-06-25 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents novel results by participants of the conference “Control theory of infinite-dimensional systems” that took place in January 2018 at the FernUniversität in Hagen. Topics include well-posedness, controllability, optimal control problems as well as stability of linear and nonlinear systems, and are covered by world-leading experts in these areas. A distinguishing feature of the contributions in this volume is the particular combination of researchers from different fields in mathematics working in an interdisciplinary fashion on joint projects in mathematical system theory. More explicitly, the fields of partial differential equations, semigroup theory, mathematical physics, graph and network theory as well as numerical analysis are all well-represented.

Download or read book Spectral Theory Of Block Operator Matrices And Applications written by Christiane Tretter and published by World Scientific. This book was released on 2008-10-15 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a wide panorama of methods to investigate the spectral properties of block operator matrices. Particular emphasis is placed on classes of block operator matrices to which standard operator theoretical methods do not readily apply: non-self-adjoint block operator matrices, block operator matrices with unbounded entries, non-semibounded block operator matrices, and classes of block operator matrices arising in mathematical physics.The main topics include: localization of the spectrum by means of new concepts of numerical range; investigation of the essential spectrum; variational principles and eigenvalue estimates; block diagonalization and invariant subspaces; solutions of algebraic Riccati equations; applications to spectral problems from magnetohydrodynamics, fluid mechanics, and quantum mechanics./a

Download or read book Control and Estimation of Systems with Input Output Delays written by Huanshui Zhang and published by Springer. This book was released on 2007-09-05 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: Time delays exist in many engineering systems such as transportation, communication, process engineering and networked control systems. In recent years, time delay systems have attracted recurring interests from research community. Much of the effort has been focused on stability analysis and stabilization of time delay systems using the so-called Lyapunov-Krasovskii functional together with a linear matrix inequality approach, which provides an efficient numerical tool for handling systems with delays in state and/or inputs. Recently, some more interesting and fundamental development for systems with input/output (i/o) delays has been made using time domain or frequency domain approaches. These approaches lead to analytical solutions to time delay problems in terms of Riccati equations or spectral factorizations. This monograph presents simple analytical solutions to control and estimation problems for systems with multiple i/o delays via elementary tools such as projection. We propose a re-organized innovation analysis approach for delay systems and establish a duality between optimal control of systems with multiple input delays and smoothing estimation for delay free systems. These appealing new techniques are applied to solve control and estimation problems for systems with multiple i/o delays and state delays under both the H2 and H-infinity performance criteria.

Download or read book Robust Control of Linear Systems and Nonlinear Control written by M. A. Kaashoek and published by Springer Science & Business Media. This book was released on 2013-03-07 with total page 657 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the second of the three volume publication containing the proceedings of the 1989 International Symposium on the Mathemat ical Theory of Networks and Systems (MTNS-89), which was held in Amsterdam, The Netherlands, June 19-23, 1989 The International Symposia MTNS focus attention on problems from system and control theory, circuit theory and signal processing, which, in general, require application of sophisticated mathematical tools, such as from function and operator theory, linear algebra and matrix theory, differential and algebraic geometry. The interaction between advanced mathematical methods and practical engineering problems of circuits, systems and control, which is typical for MTNS, turns out to be most effective and is, as these proceedings show, a continuing source of exciting advances. The second volume contains invited papers and a large selection of other symposium presentations in the vast area of robust and nonlinear control. Modern developments in robust control and H-infinity theory, for finite as well as for infinite dimensional systems, are presented. A large part of the volume is devoted to nonlinear control. Special atten tion is paid to problems in robotics. Also the general theory of nonlinear and infinite dimensional systems is discussed. A couple of papers deal with problems of stochastic control and filterina. vi Preface The titles of the two other volumes are: Realization and Modelling in System Theory (volume 1) and Signal Processing, Scattering and Operator Theory, and Numerical Methods (volume 3).

Download or read book H Control for Distributed Parameter Systems A State Space Approach written by Bert van Keulen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: VI 5.3 Proof of the measurement-feedback result. 144 5.4 Relaxation of the a priori assumptions .. 165 5.4.1 Including the feedthroughs . . . . . 165 5.4.2 How to 'remove' the regularity assumptions 174 6 Examples and conclusions 177 6.1 Delay systems in state-space . . . . . . . . . . 177 6.1.1 Dynamic controllers for delay systems. 180 184 6.1.2 A linear quadratic control problem . . 6.1.3 Duality ............... . . 189 6.2 The mixed-sensitivity problem for delay systems 192 6.2.1 Introduction and statement of the problem. 192 6.2.2 Main result .............. . 194 6.3 Conclusions and directions for future research. 200 A Stability theory 205 A.1 205 A.2 206 B Differentiability and some convergence results 207 B.l 207 208 B.2 B.3 209 209 B.4 B.5 209 B.6 211 B.7 213 214 C The invariant zeros condition C.1 214 221 D The relation between P, Q and P 221 D.1 ............ .... . Bibliography 230 239 Index Preface Control of distributed parameter systems is a fascinating and challenging top ic, from both a mathematical and an applications point of view. The same can be said about Hoc-control theory, which has become very popular lately. I am therefore pleased to present in this book a complete treatment of the state-space solution to the Hoo-control problem for a large class of distributed parameter systems.

Download or read book Controller Design for Distributed Parameter Systems written by Kirsten A. Morris and published by Springer Nature. This book was released on 2020-06-01 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses controller and estimator design for systems that vary both spatially and in time: systems like fluid flow, acoustic noise and flexible structures. It includes coverage of the selection and placement of actuators and sensors for such distributed-parameter systems. The models for distributed parameter systems are coupled ordinary/partial differential equations. Approximations to the governing equations, often of very high order, are required and this complicates both controller design and optimization of the hardware locations. Control system and estimator performance depends not only on the controller/estimator design but also on the location of the hardware. In helping the reader choose the best location for actuators and sensors, the analysis provided in this book is crucial because neither intuition nor trial-and-error is foolproof, especially where multiple sensors and actuators are required, and moving hardware can be difficult and costly. The mechatronic approach advocated, in which controller design is integrated with actuator location, can lead to better performance without increased cost. Similarly, better estimation can be obtained with carefully placed sensors. The text shows how proper hardware placement varies depending on whether, disturbances are present, whether the response should be reduced to an initial condition or whether controllability and/or observability have to be optimized. This book is aimed at non-specialists interested in learning controller design for distributed-parameter systems and the material presented has been used for student teaching. The relevant basic systems theory is presented and followed by a description of controller synthesis using lumped approximations. Numerical algorithms useful for efficient implementation in real engineering systems and practical computational challenges are also described and discussed.

Download or read book Computation and Control IV written by Kenneth L. Bowers and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of a conference of leading experts in control theory, numerical mathematics and various application areas. The conference’s interdisciplinary dialogue not only creates new mathematical tools, it often produces new research problems in the individual disciplines, aiming to develop rigorous numerical methods and computational tools for control design and analysis.

Download or read book Computation and Control II written by Kenneth L. Bowers and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a collection of papers delivered by the partici pants at the second Conference on Computation and Control held at Mon tana State University in Bozeman, Montana from August 1-7, 1990. The conference, as well as this proceedings, attests to the vitality and cohesion between the control theorist and the numerical analyst that was adver tised by the first Conference on Computation and Control in 1988. The proceedings of that initial conference was published by Birkhiiuser Boston as the first volume of this same series entitled Computation and Control, Proceedings of the Bozeman Conference, Bozeman, Montana, 1988. Control theory and numerical analysis are both, by their very nature, interdisciplinary subjects as evidenced by their interaction with other fields of mathematics and engineering. While it is clear that new control or es timation algorithms and new feedback design methodologies will need to be implemented computationally, it is likewise clear that new problems in computational mathematics arise when implementing a new generation of control algorithms. For these reasons, computational mathematics is mov ing to the forefront in recent developments in modern control theory and conversely control theory and its applications continue to be a fertile area for computationalists. This volume contains a representative cross section of the interdisciplinary blend of analytic and numerical techniques that of ten occur between advanced control design and practical numerical solution of lumped and distributed parameter systems.

Download or read book Linear Operators and Matrices written by Israel Gohberg and published by Birkhäuser. This book was released on 2012-12-06 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: In September 1998, during the 'International Workshop on Analysis and Vibrat ing Systems' held in Canmore, Alberta, Canada, it was decided by a group of participants to honour Peter Lancaster on the occasion of his 70th birthday with a volume in the series 'Operator Theory: Advances and Applications'. Friends and colleagues responded enthusiastically to this proposal and within a short time we put together the volume which is now presented to the reader. Regarding accep tance of papers we followed the usual rules of the journal 'Integral Equations and Operator Theory'. The papers are dedicated to different problems in matrix and operator theory, especially to the areas in which Peter contributed so richly. At our request, Peter agreed to write an autobiographical paper, which appears at the beginning of the volume. It continues with the list of Peter's publications. We believe that this volume will pay tribute to Peter on his outstanding achievements in different areas of mathematics. 1. Gohberg, H. Langer P ter Lancast r *1929 Operator Theory: Advances and Applications, Vol. 130, 1- 7 © 2001 Birkhiiuser Verlag Basel/Switzerland My Life and Mathematics Peter Lancaster I was born in Appleby, a small county town in the north of England, on November 14th, 1929. I had two older brothers and was to have one younger sister. My family moved around the north of England as my father's work in an insurance company required.

Download or read book Control of Distributed Parameter Systems 1989 written by M. Amouroux and published by Elsevier. This book was released on 2014-06-28 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents state-of-the-art reports on the theory, and current and future applications of control of distributed parameter systems. The papers cover the progress not only in traditional methodology and pure research in control theory, but also the rapid growth of its importance for different applications. This title will be of interest to researchers working in the areas of mathematics, automatic control, computer science and engineering.

Download or read book Modelling and Optimization of Distributed Parameter Systems Applications to engineering written by K. Malanowski and published by Springer. This book was released on 2013-06-05 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: