Dynamical Systems

Author: Albert C. J. Luo
Publisher: Springer Science & Business Media
ISBN: 9781441957542
Format: PDF, Mobi
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Dynamical Systems: Discontinuous, Stochasticity and Time-Delay provides an overview of the most recent developments in nonlinear dynamics, vibration and control. This book focuses on the most recent advances in all three areas, with particular emphasis on recent analytical, numerical and experimental research and its results. Real dynamical system problems, such as the behavior of suspension systems of railways, nonlinear vibration and applied control in coal manufacturing, along with the multifractal spectrum of LAN traffic, are discussed at length, giving the reader a sense of real-world instances where these theories are applied. Dynamical Systems: Discontinuous, Stochasticity and Time-Delay also contains material on time-delay systems as they relate to linear switching, dynamics of complex networks, and machine tools with multiple boundaries. It is the ideal book for engineers and academic researchers working in areas like mechanical and control engineering, as well as applied mathematics.

Advances in Analysis and Control of Time Delayed Dynamical Systems

Author: Jian-Qiao Sun
Publisher: World Scientific
ISBN: 9814525510
Format: PDF, ePub
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Analysis and control of time-delayed systems have been applied in a wide range of applications, ranging from mechanical, control, economic, to biological systems. Over the years, there has been a steady stream of interest in time-delayed dynamic systems, this book takes a snap shot of recent research from the world leading experts in analysis and control of dynamic systems with time delay to provide a bird's eye view of its development. The topics covered in this book include solution methods, stability analysis and control of periodic dynamic systems with time delay, bifurcations, stochastic dynamics and control, delayed Hamiltonian systems, uncertain dynamic systems with time delay, and experimental investigations of delayed structural control. Contents:Complete Quadratic Lyapunov-Krasovskii Functional: Limitations, Computational Efficiency, and Convergence (Keqin Gu)Recent Approaches for the Numerical Solution of State-Dependent Delay Differential Equations with Discontinuities (Alfredo Bellen)Engineering Applications of Time-Periodic Time-Delay Systems (Gábor Stépán)Synchronization in Delay-Coupled Complex Networks (Eckehard Schöll)Stochastic Dynamics and Optimal Control of Quasi Integrable Hamiltonian Systems with Time-Delayed Feedback Control (Weiqiu Zhu and Zhonghua Liu)Delay Induced Strong and Weak Resonances in Delayed Differential Systems (Jian Xu, Wanyong Wang)Stability and Hopf Bifurcation of Time-Delay Systems with Complex Coefficients (Zaihua Wang and Junyu Li)Estimation and Control in Time-Delayed Dynamical Systems Using the Chebyshev Spectral Continuous Time Approximation and Reduced Liapunov-Floquet Transformation (Eric A Butcher, Oleg Bobrenkov, Morad Nazari and Shahab Torkamani)Noise-Induced Dynamics of Time-Delayed Stochastic Systems (Yanfei Jin and Haiyan Hu)Some Studies on Delayed System Dynamics and Control (Guo-Pingcai, Long-Xiang Chen and Kun Liu)Switching Control of Uncertain Dynamic Systems with Time Delay (Jian-Qiao Sun, Xiao-Yan Zhang, Zhi-Chang Qin and Shun Zhong) Readership: The researchers in the community of dynamics and control including mechanical, civil, structural, aerospace, naval and electrical engineers. Graduate students pursuing research in the area of dynamics and control. Keywords:Time-Delayed Dynamical Control Systems;Stochastic Dynamics and Optimal Control SystemsKey Features:Professor Jian-Qiao Sun, of University of California-Merced is well-known for his work on stochastic nonlinear dynamical systems and cell mapping methodsProfessor Qian Ding of Tianjin University is well-known for his work on nonlinear dynamics, rotor dynamics and reduced order modeling of complex dynamical systemsThere are many books devoted to time delayed systems, as noted in the authors' proposal, but many don't do justice to control. In addition, the topic of time delayed, non-smooth systems is beginning to receive considerable attention in the literature, but not (well) addressed in any of the current books

Regularity and Stochasticity of Nonlinear Dynamical Systems

Author: Dimitri Volchenkov
Publisher: Springer
ISBN: 3319580620
Format: PDF, ePub, Mobi
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This book presents recent developments in nonlinear dynamics and physics with an emphasis on complex systems. The contributors provide recent theoretic developments and new techniques to solve nonlinear dynamical systems and help readers understand complexity, stochasticity, and regularity in nonlinear dynamical systems. This book covers integro-differential equation solvability, Poincare recurrences in ergodic systems, orientable horseshoe structure, analytical routes of periodic motions to chaos, grazing on impulsive differential equations, from chaos to order in coupled oscillators, and differential-invariant solutions for automorphic systems, inequality under uncertainty.

New Trends in Optimal Filtering and Control for Polynomial and Time Delay Systems

Author: Michael Basin
Publisher: Springer Science & Business Media
ISBN: 3540708022
Format: PDF, Docs
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0. 1 Introduction Although the general optimal solution of the ?ltering problem for nonlinear state and observation equations confused with white Gaussian noises is given by the Kushner equation for the conditional density of an unobserved state with respect to obser- tions (see [48] or [41], Theorem 6. 5, formula (6. 79) or [70], Subsection 5. 10. 5, formula (5. 10. 23)), there are a very few known examples of nonlinear systems where the Ku- ner equation can be reduced to a ?nite-dimensional closed system of ?ltering eq- tions for a certain number of lower conditional moments. The most famous result, the Kalman-Bucy ?lter [42], is related to the case of linear state and observation equations, where only two moments, the estimate itself and its variance, form a closed system of ?ltering equations. However, the optimal nonlinear ?nite-dimensional ?lter can be - tained in some other cases, if, for example, the state vector can take only a ?nite number of admissible states [91] or if the observation equation is linear and the drift term in the 2 2 state equation satis?es the Riccati equation df /dx + f = x (see [15]). The complete classi?cation of the “general situation” cases (this means that there are no special - sumptions on the structure of state and observation equations and the initial conditions), where the optimal nonlinear ?nite-dimensional ?lter exists, is given in [95].

The Stability of Dynamical Systems

Author: J. P. LaSalle
Publisher: SIAM
ISBN: 9781611970432
Format: PDF
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An introduction to aspects of the theory of dynamial systems based on extensions of Liapunov's direct method. The main ideas and structure for the theory are presented for difference equations and for the analogous theory for ordinary differential equations and retarded functional differential equations. The latest results on invariance properties for non-autonomous time-varying systems processes are presented for difference and differential equations.

Toward Analytical Chaos in Nonlinear Systems

Author: Albert C. J. Luo
Publisher: John Wiley & Sons
ISBN: 1118887174
Format: PDF, ePub
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Exact analytical solutions to periodic motions in nonlinear dynamical systems are almost not possible. Since the 18th century, one has extensively used techniques such as perturbation methods to obtain approximate analytical solutions of periodic motions in nonlinear systems. However, the perturbation methods cannot provide the enough accuracy of analytical solutions of periodic motions in nonlinear dynamical systems. So the bifurcation trees of periodic motions to chaos cannot be achieved analytically. The author has developed an analytical technique that is more effective to achieve periodic motions and corresponding bifurcation trees to chaos analytically. Toward Analytical Chaos in Nonlinear Systems systematically presents a new approach to analytically determine periodic flows to chaos or quasi-periodic flows in nonlinear dynamical systems with/without time-delay. It covers the mathematical theory and includes two examples of nonlinear systems with/without time-delay in engineering and physics. From the analytical solutions, the routes from periodic motions to chaos are developed analytically rather than the incomplete numerical routes to chaos. The analytical techniques presented will provide a better understanding of regularity and complexity of periodic motions and chaos in nonlinear dynamical systems. Key features: Presents the mathematical theory of analytical solutions of periodic flows to chaos or quasieriodic flows in nonlinear dynamical systems Covers nonlinear dynamical systems and nonlinear vibration systems Presents accurate, analytical solutions of stable and unstable periodic flows for popular nonlinear systems Includes two complete sample systems Discusses time-delayed, nonlinear systems and time-delayed, nonlinear vibrational systems Includes real world examples Toward Analytical Chaos in Nonlinear Systems is a comprehensive reference for researchers and practitioners across engineering, mathematics and physics disciplines, and is also a useful source of information for graduate and senior undergraduate students in these areas.

Sliding Mode Control of Uncertain Parameter Switching Hybrid Systems

Author: Ligang Wu
Publisher: John Wiley & Sons
ISBN: 1118862597
Format: PDF
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Presents new, state-of-the-art sliding mode control (SMC) methodologies for uncertain parameter-switching hybrid systems Sliding Mode Control of Uncertain Parameter-Switching Hybrid Systems presentsnew, state-of-the-art sliding mode control (SMC) methodologies for uncertain parameter-switching hybrid systems (including Markovian jump systems, switched hybrid systems, singular systems, stochastic systems and time-delay systems). The first part of this book establishes a unified framework for SMC of Markovian jump singular systems and proposes new SMC methodologies based on the analysis results. In the second part, the problem of SMC of switched state-delayed hybrid systems is investigated, and finally the parallel theories and techniques that have been developed are extended to deal with switched stochastic hybrid systems. Solved problems with new approaches for analysis and synthesis of continuous- and discrete-time switched hybrid systems, (including stability analysis and stabilization, dynamic output feedback control,) are also included throughout. Presents new, state-of-the-art sliding mode control (SMC) methodologies for uncertain parameter-switching hybrid systems Provides a unified, systematic framework for handling SMC problems Introduces new concepts, models and techniques Includes solved problems throughout

Qualitative Analysis and Control of Complex Neural Networks with Delays

Author: Zhanshan Wang
Publisher: Springer
ISBN: 3662474840
Format: PDF, Kindle
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This book focuses on the stability of the dynamical neural system, synchronization of the coupling neural system and their applications in automation control and electrical engineering. The redefined concept of stability, synchronization and consensus are adopted to provide a better explanation of the complex neural network. Researchers in the fields of dynamical systems, computer science, electrical engineering and mathematics will benefit from the discussions on complex systems. The book will also help readers to better understand the theory behind the control technique and its design.

Issues in Logic Operations and Computational Mathematics and Geometry 2011 Edition

Author:
Publisher: ScholarlyEditions
ISBN: 1464964785
Format: PDF, ePub
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Issues in Logic, Operations, and Computational Mathematics and Geometry: 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about Logic, Operations, and Computational Mathematics and Geometry. The editors have built Issues in Logic, Operations, and Computational Mathematics and Geometry: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Logic, Operations, and Computational Mathematics and Geometry in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Logic, Operations, and Computational Mathematics and Geometry: 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.