Download or read book Topological Obstructions to Stability and Stabilization written by Wouter Jongeneel and published by Springer Nature. This book was released on 2023-05-16 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book provides a unified overview of topological obstructions to the stability and stabilization of dynamical systems defined on manifolds and an overview that is self-contained and accessible to the control-oriented graduate student. The authors review the interplay between the topology of an attractor, its domain of attraction, and the underlying manifold that is supposed to contain these sets. They present some proofs of known results in order to highlight assumptions and to develop extensions, and they provide new results showcasing the most effective methods to cope with these obstructions to stability and stabilization. Moreover, the book shows how Borsuk’s retraction theory and the index-theoretic methodology of Krasnosel’skii and Zabreiko underlie a large fraction of currently known results. This point of view reveals important open problems, and for that reason, this book is of interest to any researcher in control, dynamical systems, topology, or related fields.
Download or read book Topological Obstructions to Stability and Stabilization written by Wouter Jongeneel and published by Springer. This book was released on 2023-05-24 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book provides a unified overview of topological obstructions to the stability and stabilization of dynamical systems defined on manifolds and an overview that is self-contained and accessible to the control-oriented graduate student. The authors review the interplay between the topology of an attractor, its domain of attraction, and the underlying manifold that is supposed to contain these sets. They present some proofs of known results in order to highlight assumptions and to develop extensions, and they provide new results showcasing the most effective methods to cope with these obstructions to stability and stabilization. Moreover, the book shows how Borsuk’s retraction theory and the index-theoretic methodology of Krasnosel’skii and Zabreiko underlie a large fraction of currently known results. This point of view reveals important open problems, and for that reason, this book is of interest to any researcher in control, dynamical systems, topology, or related fields.
Download or read book Constructive Approaches to Submanifold Stabilization written by Jan Maximilian Montenbruck and published by Logos Verlag Berlin GmbH. This book was released on 2016-07-15 with total page 115 pages. Available in PDF, EPUB and Kindle. Book excerpt: Submanifold stabilization is the problem of steering a quantity towards a desired submanifold of the space in which it evolves. This is done by controlling the system producing the quantity in an appropriate fashion. In this thesis, methods for explicitly constructing controllers which solve submanifold stabilization problems are proposed. To this end, three distinct approaches are pursued: For control systems modeled by input-affne differential equations, a construction for turning the submanifold into an asymptotically stable invariant set is presented. For controllers which shall stabilize the submanifold with minimal energy consumption, the structure of such optimal controls is investigated. For control systems modeled by input-output relationships, a framework for bounding the integral deviation of the output from the submanifold is proposed.
Download or read book Liapunov Functions and Stability in Control Theory written by Andrea Bacciotti and published by Springer Science & Business Media. This book was released on 2005-11-24 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a modern and self-contained treatment of the Liapunov method for stability analysis, in the framework of mathematical nonlinear control theory. A Particular focus is on the problem of the existence of Liapunov functions (converse Liapunov theorems) and their regularity, whose interest is especially motivated by applications to automatic control. Many recent results in this area have been collected and presented in a systematic way. Some of them are given in extended, unified versions and with new, simpler proofs. In the 2nd edition of this successful book several new sections were added and old sections have been improved, e.g., about the Zubovs method, Liapunov functions for discontinuous systems and cascaded systems. Many new examples, explanations and figures were added making this book accessible and well readable for engineers as well as mathematicians.
Download or read book Optimal Control Stabilization and Nonsmooth Analysis written by Marcio S. de Queiroz and published by Springer Science & Business Media. This book was released on 2004-04-20 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited book contains selected papers presented at the Louisiana Conference on Mathematical Control Theory (MCT'03), which brought together over 35 prominent world experts in mathematical control theory and its applications. The book forms a well-integrated exploration of those areas of mathematical control theory in which nonsmooth analysis is having a major impact. These include necessary and sufficient conditions in optimal control, Lyapunov characterizations of stability, input-to-state stability, the construction of feedback mechanisms, viscosity solutions of Hamilton-Jacobi equations, invariance, approximation theory, impulsive systems, computational issues for nonlinear systems, and other topics of interest to mathematicians and control engineers. The book has a strong interdisciplinary component and was designed to facilitate the interaction between leading mathematical experts in nonsmooth analysis and engineers who are increasingly using nonsmooth analytic tools.
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 Mathematics of Complexity and Dynamical Systems written by Robert A. Meyers and published by Springer Science & Business Media. This book was released on 2011-10-05 with total page 1885 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.
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 741 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 Introduction to the Mathematical Theory of Control written by Alberto Bressan and published by . This book was released on 2007 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Switching in Systems and Control written by Daniel Liberzon and published by Springer Science & Business Media. This book was released on 2003-06-24 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of switched systems is related to the study of hybrid systems, which has gained attention from control theorists, computer scientists, and practicing engineers. This book examines switched systems from a control-theoretic perspective, focusing on stability analysis and control synthesis of systems that combine continuous dynamics with switching events. It includes a vast bibliography and a section of technical and historical notes.
Download or read book Input to State Stability written by Andrii Mironchenko and published by Springer Nature. This book was released on 2023-03-30 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: Input-to-State Stability presents the dominating stability paradigm in nonlinear control theory that revolutionized our view on stabilization of nonlinear systems, design of robust nonlinear observers, and stability of nonlinear interconnected control systems. The applications of input-to-state stability (ISS) are manifold and include mechatronics, aerospace engineering, and systems biology. Although the book concentrates on the ISS theory of finite-dimensional systems, it emphasizes the importance of a more general view of infinite-dimensional ISS theory. This permits the analysis of more general system classes and provides new perspectives on and a better understanding of the classical ISS theory for ordinary differential equations (ODEs). Features of the book include: • a comprehensive overview of the theoretical basis of ISS; • a description of the central applications of ISS in nonlinear control theory; • a detailed discussion of the role of small-gain methods in the stability of nonlinear networks; and • an in-depth comparison of ISS for finite- and infinite-dimensional systems. The book also provides a short overview of the ISS theory for other systems classes (partial differential equations, hybrid, impulsive, and time-delay systems) and surveys the available results for the important stability properties that are related to ISS. The reader should have a basic knowledge of analysis, Lebesgue integration theory, linear algebra, and the theory of ODEs but requires no prior knowledge of dynamical systems or stability theory. The author introduces all the necessary ideas within the book. Input-to-State Stability will interest researchers and graduate students studying nonlinear control from either a mathematical or engineering background. It is intended for active readers and contains numerous exercises of varying difficulty, which are integral to the text, complementing and widening the material developed in the monograph.
Download or read book Geometric Science of Information written by Frank Nielsen and published by Springer. This book was released on 2017-10-30 with total page 877 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the Third International Conference on Geometric Science of Information, GSI 2017, held in Paris, France, in November 2017. The 101 full papers presented were carefully reviewed and selected from 113 submissions and are organized into the following subjects: statistics on non-linear data; shape space; optimal transport and applications: image processing; optimal transport and applications: signal processing; statistical manifold and hessian information geometry; monotone embedding in information geometry; information structure in neuroscience; geometric robotics and tracking; geometric mechanics and robotics; stochastic geometric mechanics and Lie group thermodynamics; probability on Riemannian manifolds; divergence geometry; non-parametric information geometry; optimization on manifold; computational information geometry; probability density estimation; session geometry of tensor-valued data; geodesic methods with constraints; applications of distance geometry.
Download or read book Lecture Notes in Algebraic Topology written by James F. Davis and published by American Mathematical Society. This book was released on 2023-05-22 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: The amount of algebraic topology a graduate student specializing in topology must learn can be intimidating. Moreover, by their second year of graduate studies, students must make the transition from understanding simple proofs line-by-line to understanding the overall structure of proofs of difficult theorems. To help students make this transition, the material in this book is presented in an increasingly sophisticated manner. It is intended to bridge the gap between algebraic and geometric topology, both by providing the algebraic tools that a geometric topologist needs and by concentrating on those areas of algebraic topology that are geometrically motivated. Prerequisites for using this book include basic set-theoretic topology, the definition of CW-complexes, some knowledge of the fundamental group/covering space theory, and the construction of singular homology. Most of this material is briefly reviewed at the beginning of the book. The topics discussed by the authors include typical material for first- and second-year graduate courses. The core of the exposition consists of chapters on homotopy groups and on spectral sequences. There is also material that would interest students of geometric topology (homology with local coefficients and obstruction theory) and algebraic topology (spectra and generalized homology), as well as preparation for more advanced topics such as algebraic $K$-theory and the s-cobordism theorem. A unique feature of the book is the inclusion, at the end of each chapter, of several projects that require students to present proofs of substantial theorems and to write notes accompanying their explanations. Working on these projects allows students to grapple with the “big picture”, teaches them how to give mathematical lectures, and prepares them for participating in research seminars. The book is designed as a textbook for graduate students studying algebraic and geometric topology and homotopy theory. It will also be useful for students from other fields such as differential geometry, algebraic geometry, and homological algebra. The exposition in the text is clear; special cases are presented over complex general statements.
Download or read book Mathematical Reviews written by and published by . This book was released on 2005 with total page 1884 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Perspectives In Scalar Curvature In 2 Volumes written by Mikhail L Gromov and published by World Scientific. This book was released on 2022-12-19 with total page 1635 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume I contains a long article by Misha Gromov based on his many years of involvement in this subject. It came from lectures delivered in Spring 2019 at IHES. There is some background given. Many topics in the field are presented, and many open problems are discussed. One intriguing point here is the crucial role played by two seemingly unrelated analytic means: index theory of Dirac operators and geometric measure theory.Very recently there have been some real breakthroughs in the field. Volume I has several survey articles written by people who were responsible for these results.For Volume II, many people in areas of mathematics and physics, whose work is somehow related to scalar curvature, were asked to write about this in any way they pleased. This gives rise to a wonderful collection of articles, some with very broad and historical views, others which discussed specific fascinating subjects.These two books give a rich and powerful view of one of geometry's very appealing sides.
Download or read book Algebraic L theory and Topological Manifolds written by Andrew Ranicki and published by Cambridge University Press. This book was released on 1992-12-10 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Assuming no previous acquaintance with surgery theory and justifying all the algebraic concepts used by their relevance to topology, Dr Ranicki explains the applications of quadratic forms to the classification of topological manifolds, in a unified algebraic framework.
Download or read book Hybrid L1 Adaptive Control written by Roshni Maiti and published by Springer Nature. This book was released on 2022-03-01 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book details the designing of hybrid control strategies for practical systems containing time varying uncertainties, disturbances, nonlinearities, unknown parameters, unmodelled dynamics, delays, etc., concurrently. In this book, the advantages of different controllers will be brought together to produce superior control performance for the practical systems. Being aware of the advantages of adaptive controller to tackle unknown constant, time varying uncertainties and time varying disturbances, a variant of adaptive controller, namely L1 adaptive controller, is hybridized with other strategies. In this book, to facilitate optimal parameter setting of the basic L1 adaptive controller, stochastic optimization technique will be hybridized with it. The stability of the optimization technique along with the controller will be guaranteed analytically with the help of spectral radius convergence. The proposed method exhibits satisfactory exploration and exploitation capabilities. Again, this book will throw light on tackling nonlinearities along with uncertainties and disturbances by hybridizing fuzzy logic with L1 adaptive controller. The performances of the designed controllers will be compared with different control methodologies to validate their effectiveness. The overall stability of the nonlinear system with the designed controller will be guaranteed with the help of fuzzy Lyapunov function to retain the zonal behaviour of the system. This fuzzy PDC-L1 adaptive controller is efficient to tackle nonlinearities and at the same time cancels unknown constant, time varying uncertainties and time varying disturbances adequately. This book will also contain four simulation case studies to validate fruitfulness of the designed controllers. To demonstrate the superior control ability of these controllers in tackling practical system, three experimental case studies will also be provided.
