Download or read book Algebraic and Geometric Methods in Nonlinear Control Theory written by M. Fliess and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 630 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point"of a Pin'. van GuIik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; ihe Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras ·are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

Download or read book Algebraic and Differential Methods for Nonlinear Control Theory written by Rafael Martínez-Guerra and published by Springer. This book was released on 2019-01-30 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a short primer in engineering mathematics with a view on applications in nonlinear control theory. In particular, it introduces some elementary concepts of commutative algebra and algebraic geometry which offer a set of tools quite different from the traditional approaches to the subject matter. This text begins with the study of elementary set and map theory. Chapters 2 and 3 on group theory and rings, respectively, are included because of their important relation to linear algebra, the group of invertible linear maps (or matrices) and the ring of linear maps of a vector space. Homomorphisms and Ideals are dealt with as well at this stage. Chapter 4 is devoted to the theory of matrices and systems of linear equations. Chapter 5 gives some information on permutations, determinants and the inverse of a matrix. Chapter 6 tackles vector spaces over a field, Chapter 7 treats linear maps resp. linear transformations, and in addition the application in linear control theory of some abstract theorems such as the concept of a kernel, the image and dimension of vector spaces are illustrated. Chapter 8 considers the diagonalization of a matrix and their canonical forms. Chapter 9 provides a brief introduction to elementary methods for solving differential equations and, finally, in Chapter 10, nonlinear control theory is introduced from the point of view of differential algebra.

Download or read book Conference on the algebraic and geometric methods in non linear control theory written by Société de mathématiques appliquées et industrielles (France). and published by . This book was released on 1985 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Methods of Algebraic Geometry in Control Theory Part I written by Peter Falb and published by Springer. This book was released on 2018-08-25 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: "An introduction to the ideas of algebraic geometry in the motivated context of system theory." Thus the author describes his textbook that has been specifically written to serve the needs of students of systems and control. Without sacrificing mathematical care, the author makes the basic ideas of algebraic geometry accessible to engineers and applied scientists. The emphasis is on constructive methods and clarity rather than abstraction. The student will find here a clear presentation with an applied flavor, of the core ideas in the algebra-geometric treatment of scalar linear system theory. The author introduces the four representations of a scalar linear system and establishes the major results of a similar theory for multivariable systems appearing in a succeeding volume (Part II: Multivariable Linear Systems and Projective Algebraic Geometry). Prerequisites are the basics of linear algebra, some simple notions from topology and the elementary properties of groups, rings, and fields, and a basic course in linear systems. Exercises are an integral part of the treatment and are used where relevant in the main body of the text. The present, softcover reprint is designed to make this classic textbook available to a wider audience. "This book is a concise development of affine algebraic geometry together with very explicit links to the applications...[and] should address a wide community of readers, among pure and applied mathematicians." —Monatshefte für Mathematik

Download or read book Algebraic Methods for Nonlinear Control Systems written by Giuseppe Conte and published by Springer Science & Business Media. This book was released on 2007-01-19 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a self-contained introduction to algebraic control for nonlinear systems suitable for researchers and graduate students. It is the first book dealing with the linear-algebraic approach to nonlinear control systems in such a detailed and extensive fashion. It provides a complementary approach to the more traditional differential geometry and deals more easily with several important characteristics of nonlinear systems.

Download or read book Nonlinear Control Systems written by G. Conte and published by Springer. This book was released on 2014-03-12 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a unique and alternative approach to the study of nonlinear control systems, with applications. The approach presented is based on the use of algebraic methods which are intrinsically linear, rather than differential geometric methods, which are more commonly found in other reference works on the subject. This allows the exposition to remain simple from a mathematical point of view, and accessible for everyone who has a good understanding of linear control theory. The book is divided into the following three parts: Part 1 is devoted to mathematical preliminaries and to the development of tools and methods for system analysis. Part 2 is concerned with solving specific control problems, including disturbance decoupling, non-interactive control, model matching and feedback linearization problems. Part 3 introduces differential algebraic notions and discusses their applications to nonlinear control and system theory. With numerous examples used to illustrate theoretical results, this self-contained and comprehensive volume will be of interest to all those who have a good basic knowledge of standard linear control systems.

Download or read book Geometric Methods in System Theory written by D.Q. Mayne and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric Methods in System Theory In automatic control there are a large number of applications of a fairly simple type for which the motion of the state variables is not free to evolve in a vector space but rather must satisfy some constraints. Examples are numerous; in a switched, lossless electrical network energy is conserved and the state evolves on an ellipsoid surface defined by x'Qx equals a constant; in the control of finite state, continuous time, Markov processes the state evolves on the set x'x = 1, xi ~ O. The control of rigid body motions and trajectory control leads to problems of this type. There has been under way now for some time an effort to build up enough control theory to enable one to treat these problems in a more or less routine way. It is important to emphasise that the ordinary vector space-linear theory often gives the wrong insight and thus should not be relied upon.

Download or read book Algebraic Methods for Nonlinear Control Systems written by Giuseppe Conte and published by Springer. This book was released on 2009-10-12 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a self-contained introduction to algebraic control for nonlinear systems suitable for researchers and graduate students. It is the first book dealing with the linear-algebraic approach to nonlinear control systems in such a detailed and extensive fashion. It provides a complementary approach to the more traditional differential geometry and deals more easily with several important characteristics of nonlinear systems.

Download or read book Geometric Control of Mechanical Systems written by Francesco Bullo and published by Springer. This book was released on 2019-06-12 with total page 727 pages. Available in PDF, EPUB and Kindle. Book excerpt: The area of analysis and control of mechanical systems using differential geometry is flourishing. This book collects many results over the last decade and provides a comprehensive introduction to the area.

Download or read book Contemporary Trends in Nonlinear Geometric Control Theory and Its Applications written by A. Anzaldo-Meneses and published by World Scientific. This book was released on 2002 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concerns contemporary trends in nonlinear geometric control theory and its applications.

Download or read book Introduction to Geometric Control written by Yuri Sachkov and published by Springer Nature. This book was released on 2022-07-02 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is an enhanced, English version of the Russian edition, published in early 2021 and is appropriate for an introductory course in geometric control theory. The concise presentation provides an accessible treatment of the subject for advanced undergraduate and graduate students in theoretical and applied mathematics, as well as to experts in classic control theory for whom geometric methods may be introduced. Theory is accompanied by characteristic examples such as stopping a train, motion of mobile robot, Euler elasticae, Dido's problem, and rolling of the sphere on the plane. Quick foundations to some recent topics of interest like control on Lie groups and sub-Riemannian geometry are included. Prerequisites include only a basic knowledge of calculus, linear algebra, and ODEs; preliminary knowledge of control theory is not assumed. The applications problems-oriented approach discusses core subjects and encourages the reader to solve related challenges independently. Highly-motivated readers can acquire working knowledge of geometric control techniques and progress to studying control problems and more comprehensive books on their own. Selected sections provide exercises to assist in deeper understanding of the material. Controllability and optimal control problems are considered for nonlinear nonholonomic systems on smooth manifolds, in particular, on Lie groups. For the controllability problem, the following questions are considered: controllability of linear systems, local controllability of nonlinear systems, Nagano–Sussmann Orbit theorem, Rashevskii–Chow theorem, Krener's theorem. For the optimal control problem, Filippov's theorem is stated, invariant formulation of Pontryagin maximum principle on manifolds is given, second-order optimality conditions are discussed, and the sub-Riemannian problem is studied in detail. Pontryagin maximum principle is proved for sub-Riemannian problems, solution to the sub-Riemannian problems on the Heisenberg group, the group of motions of the plane, and the Engel group is described.

Download or read book Perspectives in Control Theory written by B. Jakubczyk and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume contains papers based on lectures delivered during the school "Per spectives in Control Theory" held in Sielpia, Poland on September 19-24, 1988. The aim of the school was to give the state-of-the-art presentation of recent achievements as weH as perspectives in such fields of control theory as optimal control and optimization, linear systems, and nonlinear systems. Accordingly, the volume includes survey papers together with presentations of some recent results. The special emphasis is put on: - nonlinear systems (algebraic and geometric methods), - optimal control and optimization (general problems, distributed parameter systems), - linear systems (linear-quadratic problem, robust stabilization). An important feature of the school (and consequently of the volume) was its really "international" character since it brought together leading control theoriests from West and East. All together the school was attended by 108 participants from 18 countries. During the school 21 one-hour invited lectures were delivered. Moreover, five half-an-hour talks were given and 30 contributions were presented in frames of poster sessions. The school was organized and supported by: Institute of Mathematics of the Polish Academy of Sciences, Committee of Automatic Control and Robotics of the Polish Academy of Sciences, - Institute of Automatic Control, Warsaw University of Technology (as Co ordinator of the Basic Research Program R.P.I.02 "Theory of Control of Continuous Dynamic Systems and Discrete Processes" ).

Download or read book Geometrical Methods in Variational Problems written by N.A. Bobylov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained monograph presents methods for the investigation of nonlinear variational problems. These methods are based on geometric and topological ideas such as topological index, degree of a mapping, Morse-Conley index, Euler characteristics, deformation invariant, homotopic invariant, and the Lusternik-Shnirelman category. Attention is also given to applications in optimisation, mathematical physics, control, and numerical methods. Audience: This volume will be of interest to specialists in functional analysis and its applications, and can also be recommended as a text for graduate and postgraduate-level courses in these fields.

Download or read book Mathematical Control Theory written by Eduardo D. Sontag and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 543 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geared primarily to an audience consisting of mathematically advanced undergraduate or beginning graduate students, this text may additionally be used by engineering students interested in a rigorous, proof-oriented systems course that goes beyond the classical frequency-domain material and more applied courses. The minimal mathematical background required is a working knowledge of linear algebra and differential equations. The book covers what constitutes the common core of control theory and is unique in its emphasis on foundational aspects. While covering a wide range of topics written in a standard theorem/proof style, it also develops the necessary techniques from scratch. In this second edition, new chapters and sections have been added, dealing with time optimal control of linear systems, variational and numerical approaches to nonlinear control, nonlinear controllability via Lie-algebraic methods, and controllability of recurrent nets and of linear systems with bounded controls.

Download or read book Reduction of Nonlinear Control Systems written by V.I. Elkin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advances in science and technology necessitate the use of increasingly-complicated dynamic control processes. Undoubtedly, sophisticated mathematical models are also concurrently elaborated for these processes. In particular, linear dynamic control systems iJ = Ay + Bu, y E M C ]Rn, U E ]RT, (1) where A and B are constants, are often abandoned in favor of nonlinear dynamic control systems (2) which, in addition, contain a large number of equations. The solution of problems for multidimensional nonlinear control systems en counters serious difficulties, which are both mathematical and technical in nature. Therefore it is imperative to develop methods of reduction of nonlinear systems to a simpler form, for example, decomposition into systems of lesser dimension. Approaches to reduction are diverse, in particular, techniques based on approxi mation methods. In this monograph, we elaborate the most natural and obvious (in our opinion) approach, which is essentially inherent in any theory of math ematical entities, for instance, in the theory of linear spaces, theory of groups, etc. Reduction in our interpretation is based on assigning to the initial object an isomorphic object, a quotient object, and a subobject. In the theory of linear spaces, for instance, reduction consists in reducing to an isomorphic linear space, quotient space, and subspace. Strictly speaking, the exposition of any mathemat ical theory essentially begins with the introduction of these reduced objects and determination of their basic properties in relation to the initial object.

Download or read book Algebraic Geometry For Robotics And Control Theory written by Laura Menini and published by World Scientific. This book was released on 2021-09-02 with total page 615 pages. Available in PDF, EPUB and Kindle. Book excerpt: The development of inexpensive and fast computers, coupled with the discovery of efficient algorithms for dealing with polynomial equations, has enabled exciting new applications of algebraic geometry and commutative algebra. Algebraic Geometry for Robotics and Control Theory shows how tools borrowed from these two fields can be efficiently employed to solve relevant problem arising in robotics and control theory.After a brief introduction to various algebraic objects and techniques, the book first covers a wide variety of topics concerning control theory, robotics, and their applications. Specifically this book shows how these computational and theoretical methods can be coupled with classical control techniques to: solve the inverse kinematics of robotic arms; design observers for nonlinear systems; solve systems of polynomial equalities and inequalities; plan the motion of mobile robots; analyze Boolean networks; solve (possibly, multi-objective) optimization problems; characterize the robustness of linear; time-invariant plants; and certify positivity of polynomials.

Download or read book Nonlinear Control Systems written by Alberto Isidori and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to present a self-contained description of the fundamentals of the theory of nonlinear control systems, with special emphasis on the differential geometric approach. The book is intended as a graduate text as well as a reference to scientists and engineers involved in the analysis and design of feedback systems. The first version of this book was written in 1983, while I was teaching at the Department of Systems Science and Mathematics at Washington University in St. Louis. This new edition integrates my subsequent teaching experience gained at the University of Illinois in Urbana-Champaign in 1987, at the Carl Cranz Gesellschaft in Oberpfaffenhofen in 1987, at the University of California in Berkeley in 1988. In addition to a major rearrangement of the last two Chapters of the first version, this new edition incorporates two additional Chapters at a more elementary level and an exposition of some relevant research findings which have occurred since 1985. In the past few years differential geometry has proved to be an effective means of analysis and design of nonlinear control systems as it was in the past for the Laplace transform, complex variable theory and linear algebra in relation to linear systems. Synthesis problems of longstanding interest like disturbance decoupling, noninteracting control, output regulation, and the shaping of the input-output response, can be dealt with relative ease, on the basis of mathematical concepts that can be easily acquired by a control scientist.