Topological Obstructions To Stability And Stabilization PDF Download
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| Author | : Wouter Jongeneel |
| Publisher | : Springer |
| Total Pages | : 0 |
| Release | : 2023-05-24 |
| Genre | : Technology & Engineering |
| ISBN | : 9783031301322 |
Download Topological Obstructions to Stability and Stabilization Book in PDF, ePub and Kindle
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.
| Author | : Wouter Jongeneel |
| Publisher | : Springer Nature |
| Total Pages | : 134 |
| Release | : 2023-05-16 |
| Genre | : Technology & Engineering |
| ISBN | : 3031301331 |
Download Topological Obstructions to Stability and Stabilization Book in PDF, ePub and Kindle
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.
| Author | : Jan Maximilian Montenbruck |
| Publisher | : Logos Verlag Berlin GmbH |
| Total Pages | : 115 |
| Release | : 2016-07-15 |
| Genre | : Technology & Engineering |
| ISBN | : 3832542876 |
Download Constructive Approaches to Submanifold Stabilization Book in PDF, ePub and Kindle
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.
| Author | : Andrea Bacciotti |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 245 |
| Release | : 2005-11-24 |
| Genre | : Technology & Engineering |
| ISBN | : 3540273972 |
Download Liapunov Functions and Stability in Control Theory Book in PDF, ePub and Kindle
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.
| Author | : Marcio S. de Queiroz |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 380 |
| Release | : 2004-04-20 |
| Genre | : Technology & Engineering |
| ISBN | : 9783540213307 |
Download Optimal Control, Stabilization and Nonsmooth Analysis Book in PDF, ePub and Kindle
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.
| Author | : Eduardo D. Sontag |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 543 |
| Release | : 2013-11-21 |
| Genre | : Mathematics |
| ISBN | : 1461205778 |
Download Mathematical Control Theory Book in PDF, ePub and Kindle
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.
| Author | : Robert A. Meyers |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 1885 |
| Release | : 2011-10-05 |
| Genre | : Mathematics |
| ISBN | : 1461418054 |
Download Mathematics of Complexity and Dynamical Systems Book in PDF, ePub and Kindle
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.
| Author | : Francesco Bullo |
| Publisher | : Springer |
| Total Pages | : 727 |
| Release | : 2019-06-12 |
| Genre | : Science |
| ISBN | : 1489972765 |
Download Geometric Control of Mechanical Systems Book in PDF, ePub and Kindle
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.
| Author | : Alberto Bressan |
| Publisher | : |
| Total Pages | : 336 |
| Release | : 2007 |
| Genre | : Control theory |
| ISBN | : |
Download Introduction to the Mathematical Theory of Control Book in PDF, ePub and Kindle
| Author | : Daniel Liberzon |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 252 |
| Release | : 2003-06-24 |
| Genre | : Science |
| ISBN | : 0817642978 |
Download Switching in Systems and Control Book in PDF, ePub and Kindle
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.
