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Author : Vadim S. Anishchenko,Tatyana E. Vadivasova,Galina I. Strelkova
Publisher : Unknown
Page : 310 pages
File Size : 49,9 Mb
Release : 2014-07-31
Category : Electronic
ISBN : 3319068725
Author : Vadim S. Anishchenko,Tatyana E. Vadivasova,Galina I. Strelkova
Publisher : Springer
Page : 294 pages
File Size : 51,7 Mb
Release : 2014-06-16
Category : Science
ISBN : 9783319068718
This text is a short yet complete course on nonlinear dynamics of deterministic systems. Conceived as a modular set of 15 concise lectures it reflects the many years of teaching experience by the authors. The lectures treat in turn the fundamental aspects of the theory of dynamical systems, aspects of stability and bifurcations, the theory of deterministic chaos and attractor dimensions, as well as the elements of the theory of Poincare recurrences.Particular attention is paid to the analysis of the generation of periodic, quasiperiodic and chaotic self-sustained oscillations and to the issue of synchronization in such systems. This book is aimed at graduate students and non-specialist researchers with a background in physics, applied mathematics and engineering wishing to enter this exciting field of research.
Author : Gérard Iooss,Robert H. G. Helleman,Raymond Stora
Publisher : North-Holland
Page : 752 pages
File Size : 53,9 Mb
Release : 1983
Category : Science
ISBN : UOM:39015015760997
Author : Elbert Hendricks,Ole Jannerup,Paul Haase Sørensen
Publisher : Springer Science & Business Media
Page : 555 pages
File Size : 49,9 Mb
Release : 2008-10-13
Category : Technology & Engineering
ISBN : 9783540784869
Modern control theory and in particular state space or state variable methods can be adapted to the description of many different systems because it depends strongly on physical modeling and physical intuition. The laws of physics are in the form of differential equations and for this reason, this book concentrates on system descriptions in this form. This means coupled systems of linear or nonlinear differential equations. The physical approach is emphasized in this book because it is most natural for complex systems. It also makes what would ordinarily be a difficult mathematical subject into one which can straightforwardly be understood intuitively and which deals with concepts which engineering and science students are already familiar. In this way it is easy to immediately apply the theory to the understanding and control of ordinary systems. Application engineers, working in industry, will also find this book interesting and useful for this reason. In line with the approach set forth above, the book first deals with the modeling of systems in state space form. Both transfer function and differential equation modeling methods are treated with many examples. Linearization is treated and explained first for very simple nonlinear systems and then more complex systems. Because computer control is so fundamental to modern applications, discrete time modeling of systems as difference equations is introduced immediately after the more intuitive differential equation models. The conversion of differential equation models to difference equations is also discussed at length, including transfer function formulations. A vital problem in modern control is how to treat noise in control systems. Nevertheless this question is rarely treated in many control system textbooks because it is considered to be too mathematical and too difficult in a second course on controls. In this textbook a simple physical approach is made to the description of noise and stochastic disturbances which is easy to understand and apply to common systems. This requires only a few fundamental statistical concepts which are given in a simple introduction which lead naturally to the fundamental noise propagation equation for dynamic systems, the Lyapunov equation. This equation is given and exemplified both in its continuous and discrete time versions. With the Lyapunov equation available to describe state noise propagation, it is a very small step to add the effect of measurements and measurement noise. This gives immediately the Riccati equation for optimal state estimators or Kalman filters. These important observers are derived and illustrated using simulations in terms which make them easy to understand and easy to apply to real systems. The use of LQR regulators with Kalman filters give LQG (Linear Quadratic Gaussian) regulators which are introduced at the end of the book. Another important subject which is introduced is the use of Kalman filters as parameter estimations for unknown parameters. The textbook is divided into 7 chapters, 5 appendices, a table of contents, a table of examples, extensive index and extensive list of references. Each chapter is provided with a summary of the main points covered and a set of problems relevant to the material in that chapter. Moreover each of the more advanced chapters (3 - 7) are provided with notes describing the history of the mathematical and technical problems which lead to the control theory presented in that chapter. Continuous time methods are the main focus in the book because these provide the most direct connection to physics. This physical foundation allows a logical presentation and gives a good intuitive feel for control system construction. Nevertheless strong attention is also given to discrete time systems. Very few proofs are included in the book but most of the important results are derived. This method of presentation makes the text very readable and gives a good foundation for reading more rigorous texts. A complete set of solutions is available for all of the problems in the text. In addition a set of longer exercises is available for use as Matlab/Simulink ‘laboratory exercises’ in connection with lectures. There is material of this kind for 12 such exercises and each exercise requires about 3 hours for its solution. Full written solutions of all these exercises are available.
Author : Milos Marek,Igor Schreiber
Publisher : Cambridge University Press
Page : 384 pages
File Size : 53,6 Mb
Release : 1995-07-20
Category : Science
ISBN : 0521438306
This graduate text surveys both the theoretical and experimental aspects of deterministic chaotic behaviour.
Author : Michał Piórek
Publisher : Springer
Page : 132 pages
File Size : 45,7 Mb
Release : 2018-07-12
Category : Technology & Engineering
ISBN : 9783319948874
This book presents a new approach for the analysis of chaotic behavior in non-linear dynamical systems, in which output can be represented in quaternion parametrization. It offers a new family of methods for the analysis of chaos in the quaternion domain along with extensive numerical experiments performed on human motion data and artificial data. All methods and algorithms are designed to allow detection of deterministic chaos behavior in quaternion data representing the rotation of a body in 3D space. This book is an excellent reference for engineers, researchers, and postgraduate students conducting research on human gait analysis, healthcare informatics, dynamical systems with deterministic chaos or time series analysis.
Author : Heinz Georg Schuster,Wolfram Just
Publisher : John Wiley & Sons
Page : 312 pages
File Size : 54,9 Mb
Release : 2006-03-06
Category : Science
ISBN : 9783527606412
A new edition of this well-established monograph, this volume provides a comprehensive overview over the still fascinating field of chaos research. The authors include recent developments such as systems with restricted degrees of freedom but put also a strong emphasis on the mathematical foundations. Partly illustrated in color, this fourth edition features new sections from applied nonlinear science, like control of chaos, synchronisation of nonlinear systems, and turbulence, as well as recent theoretical concepts like strange nonchaotic attractors, on-off intermittency and spatio-temporal chaotic motion.
Author : Vladimir G. Ivancevic,Tijana T. Ivancevic
Publisher : Springer Science & Business Media
Page : 855 pages
File Size : 52,8 Mb
Release : 2008-05-31
Category : Science
ISBN : 9783540793571
Complex Nonlinearity: Chaos, Phase Transitions, Topology Change and Path Integrals is a book about prediction & control of general nonlinear and chaotic dynamics of high-dimensional complex systems of various physical and non-physical nature and their underpinning geometro-topological change. The book starts with a textbook-like expose on nonlinear dynamics, attractors and chaos, both temporal and spatio-temporal, including modern techniques of chaos–control. Chapter 2 turns to the edge of chaos, in the form of phase transitions (equilibrium and non-equilibrium, oscillatory, fractal and noise-induced), as well as the related field of synergetics. While the natural stage for linear dynamics comprises of flat, Euclidean geometry (with the corresponding calculation tools from linear algebra and analysis), the natural stage for nonlinear dynamics is curved, Riemannian geometry (with the corresponding tools from nonlinear, tensor algebra and analysis). The extreme nonlinearity – chaos – corresponds to the topology change of this curved geometrical stage, usually called configuration manifold. Chapter 3 elaborates on geometry and topology change in relation with complex nonlinearity and chaos. Chapter 4 develops general nonlinear dynamics, continuous and discrete, deterministic and stochastic, in the unique form of path integrals and their action-amplitude formalism. This most natural framework for representing both phase transitions and topology change starts with Feynman’s sum over histories, to be quickly generalized into the sum over geometries and topologies. The last Chapter puts all the previously developed techniques together and presents the unified form of complex nonlinearity. Here we have chaos, phase transitions, geometrical dynamics and topology change, all working together in the form of path integrals. The objective of this book is to provide a serious reader with a serious scientific tool that will enable them to actually perform a competitive research in modern complex nonlinearity. It includes a comprehensive bibliography on the subject and a detailed index. Target readership includes all researchers and students of complex nonlinear systems (in physics, mathematics, engineering, chemistry, biology, psychology, sociology, economics, medicine, etc.), working both in industry/clinics and academia.
Author : Alan S. I. Zinober
Publisher : IET
Page : 390 pages
File Size : 46,9 Mb
Release : 1990
Category : Computers
ISBN : 0863411703
Includes sections on: Sliding mode control with switching command devices. Hyperplane design and CAD of variable structure control systems. Variable structure controllers for robots. The hyperstability approach to VSCS design. Nonlinear continuous feedback for robust tracking. Control of uncertain systems with neglected dynamics. Control of infinite dimensional plants.
Author : Christoph Kawan
Publisher : Springer
Page : 270 pages
File Size : 48,5 Mb
Release : 2013-10-02
Category : Mathematics
ISBN : 9783319012889
This monograph provides an introduction to the concept of invariance entropy, the central motivation of which lies in the need to deal with communication constraints in networked control systems. For the simplest possible network topology, consisting of one controller and one dynamical system connected by a digital channel, invariance entropy provides a measure for the smallest data rate above which it is possible to render a given subset of the state space invariant by means of a symbolic coder-controller pair. This concept is essentially equivalent to the notion of topological feedback entropy introduced by Nair, Evans, Mareels and Moran (Topological feedback entropy and nonlinear stabilization. IEEE Trans. Automat. Control 49 (2004), 1585–1597). The book presents the foundations of a theory which aims at finding expressions for invariance entropy in terms of dynamical quantities such as Lyapunov exponents. While both discrete-time and continuous-time systems are treated, the emphasis lies on systems given by differential equations.
Author : Abdellatif Ben Makhlouf,Mohamed Ali Hammami,Omar Naifar
Publisher : Springer Nature
Page : 439 pages
File Size : 45,5 Mb
Release : 2023-11-06
Category : Technology & Engineering
ISBN : 9783031379703
This book presents the separation principle which is also known as the principle of separation of estimation and control and states that, under certain assumptions, the problem of designing an optimal feedback controller for a stochastic system can be solved by designing an optimal observer for the system's state, which feeds into an optimal deterministic controller for the system. Thus, the problem may be divided into two halves, which simplifies its design. In the context of deterministic linear systems, the first instance of this principle is that if a stable observer and stable state feedback are built for a linear time-invariant system (LTI system hereafter), then the combined observer and feedback are stable. The separation principle does not true for nonlinear systems in general. Another instance of the separation principle occurs in the context of linear stochastic systems, namely that an optimum state feedback controller intended to minimize a quadratic cost is optimal for the stochastic control problem with output measurements. The ideal solution consists of a Kalman filter and a linear-quadratic regulator when both process and observation noise are Gaussian. The term for this is linear-quadratic-Gaussian control. More generally, given acceptable conditions and when the noise is a martingale (with potential leaps), a separation principle, also known as the separation principle in stochastic control, applies when the noise is a martingale (with possible jumps).
Author : Mathukumalli Vidyasagar
Publisher : Unknown
Page : 498 pages
File Size : 47,5 Mb
Release : 1993-01-01
Category : Mathematics
ISBN : 0136234631
This work provides coverage of the analytical foundations of various aspects of nonlinear systems, including solutions, approximate analysis methods and stability theory from both the Lyapunov and the input-output viewpoints.
Author : El-Kebir Boukas,Zi-Kuan Liu
Publisher : Springer Science & Business Media
Page : 429 pages
File Size : 49,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461200772
Most practical processes such as chemical reactor, industrial furnace, heat exchanger, etc., are nonlinear stochastic systems, which makes their con trol in general a hard problem. Currently, there is no successful design method for this class of systems in the literature. One common alterna tive consists of linearizing the nonlinear dynamical stochastic system in the neighborhood of an operating point and then using the techniques for linear systems to design the controller. The resulting model is in general an approximation of the real behavior of a dynamical system. The inclusion of the uncertainties in the model is therefore necessary and will certainly improve the performance of the dynamical system we want to control. The control of uncertain systems has attracted a lot of researchers from the control community. This topic has in fact dominated the research effort of the control community during the last two decades, and many contributions have been reported in the literature. Some practical dynamical systems have time delay in their dynamics, which makes their control a complicated task even in the deterministic case. Recently, the class ofuncertain dynamical deterministic systems with time delay has attracted some researchers, and some interesting results have been reported in both deterministic and stochastic cases. But wecan't claim that the control problem ofthis class ofsystems is completely solved; more work must be done for this class of systems.
Author : Jan Awrejcewicz,Vadim A Krysko,Irina V Papkova,Anton V Krysko
Publisher : World Scientific
Page : 576 pages
File Size : 52,6 Mb
Release : 2016-03-14
Category : Mathematics
ISBN : 9789814719711
This book focuses on the computational analysis of nonlinear vibrations of structural members (beams, plates, panels, shells), where the studied dynamical problems can be reduced to the consideration of one spatial variable and time. The reduction is carried out based on a formal mathematical approach aimed at reducing the problems with infinite dimension to finite ones. The process also includes a transition from governing nonlinear partial differential equations to a set of finite number of ordinary differential equations. Beginning with an overview of the recent results devoted to the analysis and control of nonlinear dynamics of structural members, placing emphasis on stability, buckling, bifurcation and deterministic chaos, simple chaotic systems are briefly discussed. Next, bifurcation and chaotic dynamics of the Euler–Bernoulli and Timoshenko beams including the geometric and physical nonlinearity as well as the elastic–plastic deformations are illustrated. Despite the employed classical numerical analysis of nonlinear phenomena, the various wavelet transforms and the four Lyapunov exponents are used to detect, monitor and possibly control chaos, hyper-chaos, hyper-hyper-chaos and deep chaos exhibited by rectangular plate-strips and cylindrical panels. The book is intended for post-graduate and doctoral students, applied mathematicians, physicists, teachers and lecturers of universities and companies dealing with a nonlinear dynamical system, as well as theoretically inclined engineers of mechanical and civil engineering. Contents:Bifurcational and Chaotic Dynamics of Simple Structural Members:BeamsPlatesPanelsShellsIntroduction to Fractal Dynamics:Cantor Set and Cantor DustKoch Snowflake1D MapsSharkovsky's TheoremJulia SetMandelbrot's SetIntroduction to Chaos and Wavelets:Routes to ChaosQuantifying Chaotic DynamicsSimple Chaotic Models:IntroductionAutonomous SystemsNon-Autonomous SystemsDiscrete and Continuous Dissipative Systems:IntroductionLinear FrictionNonlinear FrictionHysteretic FrictionImpact DampingDamping in Continuous 1D SystemsEuler-Bernoulli Beams:IntroductionPlanar BeamsLinear Planar Beams and Stationary Temperature FieldsCurvilinear Planar Beams and Stationary Temperature and Electrical FieldsBeams with Elasto-Plastic DeformationsMulti-Layer BeamsTimoshenko and Sheremetev-Pelekh Beams:The Timoshenko BeamsThe Sheremetev-Pelekh BeamsConcluding RemarksPanels:Infinite Length PanelsCylindrical Panels of Infinite LengthPlates and Shells:Plates with Initial ImperfectionsFlexible Axially-Symmetric Shells Readership: Post-graduate and doctoral students, applied mathematicians, physicists, mechanical and civil engineers. Key Features:Includes fascinating and rich dynamics exhibited by simple structural members and by the solution properties of the governing 1D non-linear PDEs, suitable for applied mathematicians and physicistsCovers a wide variety of the studied PDEs, their validated reduction to ODEs, classical and non-classical methods of analysis, influence of various boundary conditions and control parameters, as well as the illustrative presentation of the obtained results in the form of colour 2D and 3D figures and vibration type charts and scalesContains originally discovered, illustrated and discussed novel and/or modified classical scenarios of transition from regular to chaotic dynamics exhibited by 1D structural members, showing a way to control chaotic and bifurcational dynamics, with directions to study other dynamical systems modeled by chains of nonlinear oscillators
Author : Kevin L. Moore
Publisher : Springer Science & Business Media
Page : 158 pages
File Size : 49,5 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781447119128
The material presented in this book addresses the analysis and design of learning control systems. It begins with an introduction to the concept of learning control, including a comprehensive literature review. The text follows with a complete and unifying analysis of the learning control problem for linear LTI systems using a system-theoretic approach which offers insight into the nature of the solution of the learning control problem. Additionally, several design methods are given for LTI learning control, incorporating a technique based on parameter estimation and a one-step learning control algorithm for finite-horizon problems. Further chapters focus upon learning control for deterministic nonlinear systems, and a time-varying learning controller is presented which can be applied to a class of nonlinear systems, including the models of typical robotic manipulators. The book concludes with the application of artificial neural networks to the learning control problem. Three specific ways to neural nets for this purpose are discussed, including two methods which use backpropagation training and reinforcement learning. The appendices in the book are particularly useful because they serve as a tutorial on artificial neural networks.