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This book provides a self-contained presentation of the physical and mathematical laws governing complex systems. Complex systems arising in natural, engineering, environmental, life and social sciences are approached from a unifying point of view using an array of methodologies such as microscopic and macroscopic level formulations, deterministic and probabilistic tools, modeling and simulation. The book can be used as a textbook by graduate students, researchers and teachers in science, as well as non-experts who wish to have an overview of one of the most open, markedly interdisciplinary an

Nonlinear systems. --- System analysis. --- Computational complexity. --- Nonlinear theories. --- Nonlinear problems --- Nonlinearity (Mathematics) --- Calculus --- Mathematical analysis --- Mathematical physics --- Complexity, Computational --- Electronic data processing --- Machine theory --- Network analysis --- Network science --- Network theory --- Systems analysis --- System theory --- Mathematical optimization --- Systems, Nonlinear --- Nonlinear systems --- System analysis --- Computational complexity --- Nonlinear theories

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There has been a great deal of excitement in the last ten years over the emer­ gence of new mathematical techniques for the analysis and control of nonlinear systems: Witness the emergence of a set of simplified tools for the analysis of bifurcations, chaos, and other complicated dynamical behavior and the develop­ ment of a comprehensive theory of geometric nonlinear control. Coupled with this set of analytic advances has been the vast increase in computational power available for both the simulation and visualization of nonlinear systems as well as for the implementation in real time of sophisticated, real-time nonlinear control laws. Thus, technological advances havebolstered the impact of analytic advances and produced a tremendous variety of new problems and applications that are nonlinear in an essential way. Nonlinear controllaws have been implemented for sophisticated flight control systems on board helicopters, and vertical take offand landing aircraft; adaptive, nonlinearcontrollaws havebeen implementedfor robot manipulators operating either singly, or in cooperation on a multi-fingered robot hand; adaptive control laws have been implemented forjetengines andautomotive fuel injection systems, as well as for automated highway systems and air traffic management systems, to mention a few examples. Bifurcation theory has been used to explain and understand the onset of fiutterin the dynamics of aircraft wing structures, the onset of oscillations in nonlinear circuits, surge and stall in aircraft engines, voltage collapse in a power transmission network.

Differential geometry. Global analysis --- Nonlinear systems --- System analysis --- Systèmes non linéaires --- Analyse de systèmes --- System Analysis --- 519.71 --- 681.511.4 --- #TELE:SISTA --- Network theory --- Systems analysis --- System theory --- Mathematical optimization --- Systems, Nonlinear --- Control systems theory: mathematical aspects --- Non-linear control systems --- Nonlinear systems. --- System analysis. --- 681.511.4 Non-linear control systems --- 519.71 Control systems theory: mathematical aspects --- Systèmes non linéaires --- Analyse de systèmes --- Network analysis --- Network science --- Calculus of variations. --- Calculus of Variations and Optimal Control; Optimization. --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima

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This book provides engineers and scientists in academia and industry with a thorough understanding of the underlying principles of nonlinear system identification. It equips them to apply the models and methods discussed to real problems with confidence, while also making them aware of potential difficulties that may arise in practice. Moreover, the book is self-contained, requiring only a basic grasp of matrix algebra, signals and systems, and statistics. Accordingly, it can also serve as an introduction to linear system identification, and provides a practical overview of the major optimization methods used in engineering. The focus is on gaining an intuitive understanding of the subject and the practical application of the techniques discussed. The book is not written in a theorem/proof style; instead, the mathematics is kept to a minimum, and the ideas covered are illustrated with numerous figures, examples, and real-world applications. In the past, nonlinear system identification was a field characterized by a variety of ad-hoc approaches, each applicable only to a very limited class of systems. With the advent of neural networks, fuzzy models, Gaussian process models, and modern structure optimization techniques, a much broader class of systems can now be handled. Although one major aspect of nonlinear systems is that virtually every one is unique, tools have since been developed that allow each approach to be applied to a wide variety of systems. .

Statistical physics. --- Control engineering. --- Robotics. --- Mechatronics. --- Computational complexity. --- Calculus of variations. --- Computer simulation. --- Applications of Nonlinear Dynamics and Chaos Theory. --- Control and Systems Theory. --- Control, Robotics, Mechatronics. --- Complexity. --- Calculus of Variations and Optimal Control; Optimization. --- Simulation and Modeling. --- Control engineering --- Control equipment --- Control theory --- Engineering instruments --- Automation --- Programmable controllers --- Physics --- Mathematical statistics --- Computer modeling --- Computer models --- Modeling, Computer --- Models, Computer --- Simulation, Computer --- Electromechanical analogies --- Mathematical models --- Simulation methods --- Model-integrated computing --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Complexity, Computational --- Electronic data processing --- Machine theory --- Mechanical engineering --- Microelectronics --- Microelectromechanical systems --- Statistical methods --- System identification. --- Nonlinear systems. --- Automatic control engineering. --- Systems, Nonlinear --- System theory --- Identification, System --- System analysis

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Some of the most common dynamic phenomena that arise in engineering practice—actuator and sensor delays—fall outside the scope of standard finite-dimensional system theory. The first attempt at infinite-dimensional feedback design in the field of control systems—the Smith predictor—has remained limited to linear finite-dimensional plants over the last five decades. Shedding light on new opportunities in predictor feedback, this book significantly broadens the set of techniques available to a mathematician or engineer working on delay systems. The book is a collection of tools and techniques that make predictor feedback ideas applicable to nonlinear systems, systems modeled by PDEs, systems with highly uncertain or completely unknown input/output delays, and systems whose actuator or sensor dynamics are modeled by more general hyperbolic or parabolic PDEs, rather than by pure delay. Specific features and topics include: * A construction of explicit Lyapunov functionals, which can be used in control design or stability analysis, leading to a resolution of several long-standing problems in predictor feedback. * A detailed treatment of individual classes of problems—nonlinear ODEs, parabolic PDEs, first-order hyperbolic PDEs, second-order hyperbolic PDEs, known time-varying delays, unknown constant delays—will help the reader master the techniques presented. * Numerous examples ease a student new to delay systems into the topic. * Minimal prerequisites: the basics of function spaces and Lyapunov theory for ODEs. * The basics of Poincaré and Agmon inequalities, Lyapunov and input-to-state stability, parameter projection for adaptive control, and Bessel functions are summarized in appendices for the reader’s convenience. Delay Compensation for Nonlinear, Adaptive, and PDE Systems is an excellent reference for graduate students, researchers, and practitioners in mathematics, systems control, as well as chemical, mechanical, electrical, computer, aerospace, and civil/structural engineering. Parts of the book may be used in graduate courses on general distributed parameter systems, linear delay systems, PDEs, nonlinear control, state estimator and observers, adaptive control, robust control, or linear time-varying systems.

Delay lines. --- Feedback control systems. --- Nonlinear systems. --- Systems engineering. --- Feedback control systems --- Nonlinear systems --- Delay lines --- Adaptive control systems --- Civil & Environmental Engineering --- Mechanical Engineering --- Operations Research --- Mechanical Engineering - General --- Engineering & Applied Sciences --- Mathematical models --- Adaptive control systems. --- Mathematical models. --- Systems, Nonlinear --- Feedback mechanisms --- Feedback systems --- Self-adaptive control systems --- Mathematics. --- Differential equations. --- Partial differential equations. --- Applied mathematics. --- Engineering mathematics. --- System theory. --- Mechanical engineering. --- Control engineering. --- Applications of Mathematics. --- Systems Theory, Control. --- Control. --- Partial Differential Equations. --- Ordinary Differential Equations. --- Mechanical Engineering. --- System theory --- Automatic control --- Automation --- Discrete-time systems --- Feedforward control systems --- Artificial intelligence --- Self-organizing systems --- Systems theory. --- Differential equations, partial. --- Differential Equations. --- Control and Systems Theory. --- Engineering, Mechanical --- Engineering --- Machinery --- Steam engineering --- 517.91 Differential equations --- Differential equations --- Partial differential equations --- Math --- Science --- Control engineering --- Control equipment --- Control theory --- Engineering instruments --- Programmable controllers --- Systems, Theory of --- Systems science --- Engineering analysis --- Mathematical analysis --- Philosophy --- Mathematics --- Feedback control systems - Mathematical models --- Adaptive control systems - Mathematical models