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Author : Madjid Kidouche
Publisher :
ISBN 13 :
Total Pages : 82 pages
Book Rating : 4.:/5 (244 download)
Download or read book Application of Graph Theory to Stability of Nonlinear Systems written by Madjid Kidouche and published by . This book was released on 1986 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Yongduan Song
Publisher : Springer
ISBN 13 : 3030049728
Total Pages : 197 pages
Book Rating : 4.0/5 (3 download)
Download or read book Cooperative Control of Nonlinear Networked Systems written by Yongduan Song and published by Springer. This book was released on 2019-01-01 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cooperative Control of Nonlinear Networked Systems is concerned with the distributed cooperative control of multiple networked nonlinear systems in the presence of unknown non-parametric uncertainties and non-vanishing disturbances under certain communication conditions. It covers stability analysis tools and distributed control methods for analyzing and synthesizing nonlinear networked systems. The book presents various solutions to cooperative control problems of multiple networked nonlinear systems on graphs. The book includes various examples with segments of MATLAB® codes for readers to verify, validate, and replicate the results. The authors present a series of new control results for nonlinear networked systems subject to both non-parametric and non-vanishing uncertainties, including the cooperative uniformly ultimately bounded (CUUB) result, finite-time stability result, and finite-time cooperative uniformly ultimately bounded (FT-CUUB) result. With some mathematical tools, such as algebraic graph theory and certain aspects of matrix analysis theory introduced by the authors, the readers can obtain a deeper understanding of the roles of matrix operators as mathematical machinery for cooperative control design for multi-agent systems. Cooperative Control of Nonlinear Networked Systems is a valuable source of information for researchers and engineers in cooperative adaptive control, as its technical contents are presented with examples in full analytical and numerical detail, and graphically illustrated for easy-to-understand results. Scientists in research institutes and academics in universities working on nonlinear systems, adaptive control and distributed control will find the book of interest, as it contains multi-disciplinary problems and covers different areas of research.
Author : Richard Clay
Publisher :
ISBN 13 :
Total Pages : 312 pages
Book Rating : 4.3/5 (91 download)
Download or read book Nonlinear Networks and Systems written by Richard Clay and published by . This book was released on 1971 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Vangipuram Lakshmikantham
Publisher : Birkhäuser
ISBN 13 : 3319272004
Total Pages : 339 pages
Book Rating : 4.3/5 (192 download)
Download or read book Stability Analysis of Nonlinear Systems written by Vangipuram Lakshmikantham and published by Birkhäuser. This book was released on 2015-12-29 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book investigates stability theory in terms of two different measure, exhibiting the advantage of employing families of Lyapunov functions and treats the theory of a variety of inequalities, clearly bringing out the underlying theme. It also demonstrates manifestations of the general Lyapunov method, showing how this technique can be adapted to various apparently diverse nonlinear problems. Furthermore it discusses the application of theoretical results to several different models chosen from real world phenomena, furnishing data that is particularly relevant for practitioners. Stability Analysis of Nonlinear Systems is an invaluable single-sourse reference for industrial and applied mathematicians, statisticians, engineers, researchers in the applied sciences, and graduate students studying differential equations.
Author : Marcio de Queiroz
Publisher : John Wiley & Sons
ISBN 13 : 1118887441
Total Pages : 204 pages
Book Rating : 4.1/5 (188 download)
Download or read book Formation Control of Multi-Agent Systems written by Marcio de Queiroz and published by John Wiley & Sons. This book was released on 2019-04-08 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Formation Control of Multi-Agent Systems: A Graph Rigidity Approach Marcio de Queiroz, Louisiana State University, USA Xiaoyu Cai, FARO Technologies, USA Matthew Feemster, U.S. Naval Academy, USA A comprehensive guide to formation control of multi-agent systems using rigid graph theory This book is the first to provide a comprehensive and unified treatment of the subject of graph rigidity-based formation control of multi-agent systems. Such systems are relevant to a variety of emerging engineering applications, including unmanned robotic vehicles and mobile sensor networks. Graph theory, and rigid graphs in particular, provides a natural tool for describing the multi-agent formation shape as well as the inter-agent sensing, communication, and control topology. Beginning with an introduction to rigid graph theory, the contents of the book are organized by the agent dynamic model (single integrator, double integrator, and mechanical dynamics) and by the type of formation problem (formation acquisition, formation manoeuvring, and target interception). The book presents the material in ascending level of difficulty and in a self-contained manner; thus, facilitating reader understanding. Key features: Uses the concept of graph rigidity as the basis for describing the multi-agent formation geometry and solving formation control problems. Considers different agent models and formation control problems. Control designs throughout the book progressively build upon each other. Provides a primer on rigid graph theory. Combines theory, computer simulations, and experimental results. Formation Control of Multi-Agent Systems: A Graph Rigidity Approach is targeted at researchers and graduate students in the areas of control systems and robotics. Prerequisite knowledge includes linear algebra, matrix theory, control systems, and nonlinear systems.
Author : I. Ya Kats
Publisher : CRC Press
ISBN 13 : 0203218892
Total Pages : 256 pages
Book Rating : 4.2/5 (32 download)
Download or read book Stability and Stabilization of Nonlinear Systems with Random Structures written by I. Ya Kats and published by CRC Press. This book was released on 2002-08-22 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear systems with random structures arise quite frequently as mathematical models in diverse disciplines. This monograph presents a systematic treatment of stability theory and the theory of stabilization of nonlinear systems with random structure in terms of new developments in the direct Lyapunov's method. The analysis focuses on dynamic sys
Author : Derek P. Atherton
Publisher : John Wiley & Sons
ISBN 13 :
Total Pages : 254 pages
Book Rating : 4.3/5 (91 download)
Download or read book Stability of Nonlinear Systems written by Derek P. Atherton and published by John Wiley & Sons. This book was released on 1981 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Shuli Guo
Publisher : Springer
ISBN 13 : 9811089086
Total Pages : 268 pages
Book Rating : 4.8/5 (11 download)
Download or read book Stability and Control of Nonlinear Time-varying Systems written by Shuli Guo and published by Springer. This book was released on 2018-04-12 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents special systems derived from industrial models, including the complex saturation nonlinear functions and the delay nonlinear functions. It also presents typical methods, such as the classical Liapunov and Integral Inequalities methods. Providing constructive qualitative and stability conditions for linear systems with saturated inputs in both global and local contexts, it offers practitioners more concise model systems for modern saturation nonlinear techniques, which have the potential for future applications. This book is a valuable guide for researchers and graduate students in the fields of mathematics, control, and engineering.
Author : Anatoly A. Martynyuk
Publisher : Birkhäuser
ISBN 13 : 3319422138
Total Pages : 233 pages
Book Rating : 4.3/5 (194 download)
Download or read book Stability Theory for Dynamic Equations on Time Scales written by Anatoly A. Martynyuk and published by Birkhäuser. This book was released on 2016-09-22 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is a first in the world to present three approaches for stability analysis of solutions of dynamic equations. The first approach is based on the application of dynamic integral inequalities and the fundamental matrix of solutions of linear approximation of dynamic equations. The second is based on the generalization of the direct Lyapunovs method for equations on time scales, using scalar, vector and matrix-valued auxiliary functions. The third approach is the application of auxiliary functions (scalar, vector, or matrix-valued ones) in combination with differential dynamic inequalities. This is an alternative comparison method, developed for time continuous and time discrete systems.In recent decades, automatic control theory in the study of air- and spacecraft dynamics and in other areas of modern applied mathematics has encountered problems in the analysis of the behavior of solutions of time continuous-discrete linear and/or nonlinear equations of perturbed motion. In the book “Men of Mathematics,” 1937, E.T.Bell wrote: “A major task of mathematics today is to harmonize the continuous and the discrete, to include them in one comprehensive mathematics, and to eliminate obscurity from both.”Mathematical analysis on time scales accomplishes exactly this. This research has potential applications in such areas as theoretical and applied mechanics, neurodynamics, mathematical biology and finance among others.
Author : Fred Roberts
Publisher : Springer Science & Business Media
ISBN 13 : 1468463810
Total Pages : 345 pages
Book Rating : 4.4/5 (684 download)
Download or read book Applications of Combinatorics and Graph Theory to the Biological and Social Sciences written by Fred Roberts and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This IMA Volume in Mathematics and its Applications Applications of Combinatorics and Graph Theory to the Biological and Social Sciences is based on the proceedings of a workshop which was an integral part of the 1987-88 IMA program on APPLIED COMBINATORICS. We are grateful to the Scientific Committee: Victor Klee (Chairman), Daniel Kleitman, Dijen Ray-Chaudhuri and Dennis Stanton for planning and implementing an exciting and stimulating year long program. We especially thank the Workshop Organizers, Joel Cohen and Fred Roberts, for organizing a workshop which brought together many of the major figures in a variety of research fields connected with the application of combinatorial ideas to the social and biological sciences. A vner Friedman Willard Miller APPLICATIONS OF COMBINATORICS AND GRAPH THEORY TO THE BIOLOGICAL AND SOCIAL SCIENCES: SEVEN FUNDAMENTAL IDEAS FRED S. RoBERTS* Abstract. To set the stage for the other papers in this volume, seven fundamental concepts which arise in the applications of combinatorics and graph theory in the biological and social sciences are described. These ideas are: RNA chains as "words" in a 4 letter alphabet; interval graphs; competition graphs or niche overlap graphs; qualitative stability; balanced signed graphs; social welfare functions; and semiorders. For each idea, some basic results are presented, some recent results are given, and some open problems are mentioned.
Author : Albert C.J. Luo
Publisher : Springer
ISBN 13 : 3319266306
Total Pages : 210 pages
Book Rating : 4.3/5 (192 download)
Download or read book Mathematical Modeling and Applications in Nonlinear Dynamics written by Albert C.J. Luo and published by Springer. This book was released on 2016-01-28 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book covers nonlinear physical problems and mathematical modeling, including molecular biology, genetics, neurosciences, artificial intelligence with classical problems in mechanics and astronomy and physics. The chapters present nonlinear mathematical modeling in life science and physics through nonlinear differential equations, nonlinear discrete equations and hybrid equations. Such modeling can be effectively applied to the wide spectrum of nonlinear physical problems, including the KAM (Kolmogorov-Arnold-Moser (KAM)) theory, singular differential equations, impulsive dichotomous linear systems, analytical bifurcation trees of periodic motions, and almost or pseudo- almost periodic solutions in nonlinear dynamical systems.
Author : D. Logofet
Publisher : CRC Press
ISBN 13 : 1351091220
Total Pages : 383 pages
Book Rating : 4.3/5 (51 download)
Download or read book Matrices and Graphs Stability Problems in Mathematical Ecology written by D. Logofet and published by CRC Press. This book was released on 2018-02-01 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intuitive ideas of stability in dynamics of a biological population, community, or ecosystem can be formalized in the framework of corresponding mathematical models. These are often represented by systems of ordinary differential equations or difference equations. Matrices and Graphs covers achievements in the field using concepts from matrix theory and graph theory. The book effectively surveys applications of mathematical results pertinent to issues of theoretical and applied ecology. The only mathematical prerequisite for using Matrices and Graphs is a working knowledge of linear algebra and matrices. The book is ideal for biomathematicians, ecologists, and applied mathematicians doing research on dynamic behavior of model populations and communities consisting of multi-component systems. It will also be valuable as a text for a graduate-level topics course in applied math or mathematical ecology.
Author : Ivana Kovacic
Publisher : John Wiley & Sons
ISBN 13 : 0470977833
Total Pages : 335 pages
Book Rating : 4.4/5 (79 download)
Download or read book The Duffing Equation written by Ivana Kovacic and published by John Wiley & Sons. This book was released on 2011-02-11 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Duffing Equation: Nonlinear Oscillators and their Behaviour brings together the results of a wealth of disseminated research literature on the Duffing equation, a key engineering model with a vast number of applications in science and engineering, summarizing the findings of this research. Each chapter is written by an expert contributor in the field of nonlinear dynamics and addresses a different form of the equation, relating it to various oscillatory problems and clearly linking the problem with the mathematics that describe it. The editors and the contributors explain the mathematical techniques required to study nonlinear dynamics, helping the reader with little mathematical background to understand the text. The Duffing Equation provides a reference text for postgraduate and students and researchers of mechanical engineering and vibration / nonlinear dynamics as well as a useful tool for practising mechanical engineers. Includes a chapter devoted to historical background on Georg Duffing and the equation that was named after him. Includes a chapter solely devoted to practical examples of systems whose dynamic behaviour is described by the Duffing equation. Contains a comprehensive treatment of the various forms of the Duffing equation. Uses experimental, analytical and numerical methods as well as concepts of nonlinear dynamics to treat the physical systems in a unified way.
Author : Paul Glendinning
Publisher : Cambridge University Press
ISBN 13 : 9780521425667
Total Pages : 408 pages
Book Rating : 4.4/5 (256 download)
Download or read book Stability, Instability and Chaos written by Paul Glendinning and published by Cambridge University Press. This book was released on 1994-11-25 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to nonlinear differential equations which equips undergraduate students with the know-how to appreciate stability theory and bifurcation.
Author : V. Lakshmikantham
Publisher : Elsevier
ISBN 13 : 1483272249
Total Pages : 717 pages
Book Rating : 4.4/5 (832 download)
Download or read book Nonlinear Systems and Applications written by V. Lakshmikantham and published by Elsevier. This book was released on 2014-05-12 with total page 717 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Systems and Applications: An International Conference contains the proceedings of an International Conference on Nonlinear Systems and Applications held at the University of Texas at Arlington, on July 19-23, 1976. The conference provided a forum for reviewing advances in nonlinear systems and their applications and tackled a wide array of topics ranging from abstract evolution equations and nonlinear semigroups to controllability and reachability. Various methods used in solving equations are also discussed, including approximation techniques for delay systems. Most of the applications are in the area of the life sciences. Comprised of 59 chapters, this book begins with a discussion on monotonically convergent upper and lower bounds for classes of conflicting populations, followed by an analysis of constrained problems. The reader is then introduced to approximation techniques for delay systems in biological models; differential inequalities for Liapunov functions; and stability or chaos in discrete epidemic models. Subsequent chapters deal with nonlinear boundary value problems for elliptic systems; bounds for solutions of reaction-diffusion equations; monotonicity and measurability; and periodic solutions of some integral equations from the theory of epidemics. This monograph will be helpful to students, practitioners, and researchers in the field of mathematics.
Author : Andrei A. Agrachev
Publisher : Springer
ISBN 13 : 3540776532
Total Pages : 368 pages
Book Rating : 4.5/5 (47 download)
Download or read book Nonlinear and Optimal Control Theory written by Andrei A. Agrachev and published by Springer. This book was released on 2008-06-24 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: The lectures gathered in this volume present some of the different aspects of Mathematical Control Theory. Adopting the point of view of Geometric Control Theory and of Nonlinear Control Theory, the lectures focus on some aspects of the Optimization and Control of nonlinear, not necessarily smooth, dynamical systems. Specifically, three of the five lectures discuss respectively: logic-based switching control, sliding mode control and the input to the state stability paradigm for the control and stability of nonlinear systems. The remaining two lectures are devoted to Optimal Control: one investigates the connections between Optimal Control Theory, Dynamical Systems and Differential Geometry, while the second presents a very general version, in a non-smooth context, of the Pontryagin Maximum Principle. The arguments of the whole volume are self-contained and are directed to everyone working in Control Theory. They offer a sound presentation of the methods employed in the control and optimization of nonlinear dynamical systems.
Author : Wiktor Eckhaus
Publisher : Springer
ISBN 13 :
Total Pages : 136 pages
Book Rating : 4.:/5 (44 download)
Download or read book Studies in Non-Linear Stability Theory written by Wiktor Eckhaus and published by Springer. This book was released on 1965 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: Non-linear stability problems formulated in terms of non-linear partial differential equations have only recently begun to attract attention and it will probably take some time before our understanding of those problems reaches some degree of maturity. The passage from the more classical linear analysis to a non-linear analysis increases the mathematical complexity of the stability theory to a point where it may become discouraging, while some of the more usual mathematical methods lose their applicability. Although considerable progress has been made in recent years, notably in the field of fluid mechanics, much still remains to be done before a more permanent outline of the subject can be established. I have not tried to present in this monograph an account of what has been accomplished, since the rapidly changing features of the field make the periodical literature a more appropriate place for such a review. The aim of this book is to present one particular line of research, originally developed in a series of papers published in 'Journal de Mecanique' 1962-1963, in which I attempted to construct a mathematical theory for certain classes of non-linear stability problems, and to gain some understanding of the non-linear phenomena which are involved. The opportunity to collect the material in this volume has permitted a more coherent presentation, while various points of the analysis have been developed in greater detaiL I hope that a more unified form of the theory has thus been achieved.
