This volume presents a systematic and unified treatment of Leray-Schauder continuation theorems in nonlinear analysis. In particular, fixed point theory is established for many classes of maps, such as contractive, non-expansive, accretive, and compact maps, to name but a few. This book also presents coincidence and multiplicity results. Many appli
Nature-inspired Optimization Algorithms for Fuzzy Controlled Servo Systems suits the general need of a book that explains the major issues to fuzzy control in servo systems without any solid mathematical prerequisite. In addition, pertinent information on nature-inspired optimization algorithms is offered. The book is intended to rapidly make intelligible notions of fuzzy set theory and fuzzy control to readers with limited experience. The attractive analysis and design methodologies dedicated to fuzzy controllers are accompanied by applications to servo systems and case studies in fuzzy controlled servo systems are organized in a special chapter of this book, and allow simple implementations of low-cost automation solutions. The theoretical approaches presented throughout the book are validated by the illustration of digital simulation results and real-time experimental results as well. This book aims at a large category of audience including graduate students, engineers (designers, practitioners and researchers), and everyone who faces challenging control problems. Gives a merge between classical and modern approaches to fuzzy control Presents in a unified structure from the point of view of a control engineer the essential aspects regarding fuzzy control in servo systems Makes intelligible notions of fuzzy set theory and fuzzy control to readers with limited experience
This book categorizes the wide area of data-driven model-free controllers, reveals the exact benefits of such controllers, gives the in-depth theory and mathematical proofs behind them, and finally discusses their applications. Each chapter includes a section for presenting the theory and mathematical definitions of one of the above mentioned algorithms. The second section of each chapter is dedicated to the examples and applications of the corresponding control algorithms in practical engineering problems. This book proposes to avoid complex mathematical equations, being generic as it includes several types of data-driven model-free controllers, such as Iterative Feedback Tuning controllers, Model-Free Controllers (intelligent PID controllers), Model-Free Adaptive Controllers, model-free sliding mode controllers, hybrid model‐free and model‐free adaptive‐Virtual Reference Feedback Tuning controllers, hybrid model-free and model-free adaptive fuzzy controllers and cooperative model-free controllers. The book includes the topic of optimal model-free controllers, as well. The optimal tuning of model-free controllers is treated in the chapters that deal with Iterative Feedback Tuning and Virtual Reference Feedback Tuning. Moreover, the extension of some model-free control algorithms to the consensus and formation-tracking problem of multi-agent dynamic systems is provided. This book can be considered as a textbook for undergraduate and postgraduate students, as well as a professional reference for industrial and academic researchers, attracting the readers from both industry and academia.
The text is intended for students who wish a concise and rapid introduction to some main topics in PDEs, necessary for understanding current research, especially in nonlinear PDEs. Organized on three parts, the book guides the reader from fundamental classical results, to some aspects of the modern theory and furthermore, to some techniques of nonlinear analysis. Compared to other introductory books in PDEs, this work clearly explains the transition from classical to generalized solutions and the natural way in which Sobolev spaces appear as completions of spaces of continuously differentiable functions with respect to energetic norms. Also, special attention is paid to the investigation of the solution operators associated to elliptic, parabolic and hyperbolic non-homogeneous equations anticipating the operator approach of nonlinear boundary value problems. Thus the reader is made to understand the role of linear theory for the analysis of nonlinear problems.
This volume presents a systematic and unified treatment of Leray-Schauder continuation theorems in nonlinear analysis. In particular, fixed point theory is established for many classes of maps, such as contractive, non-expansive, accretive, and compact maps, to name but a few. This book also presents coincidence and multiplicity results. Many applications of current interest in the theory of nonlinear differential equations are presented to complement the theory. The text is essentially self-contained, so it may also be used as an introduction to topological methods in nonlinear analysis. This volume will appeal to graduate students and researchers in mathematical analysis and its applications.
This introductory text combines models from physics and biology with rigorous reasoning in describing the theory of ordinary differential equations along with applications and computer simulations with Maple. Offering a concise course in the theory of ordinary differential equations, it also enables the reader to enter the field of computer simulations. Thus, it is a valuable read for students in mathematics as well as in physics and engineering. It is also addressed to all those interested in mathematical modeling with ordinary differential equations and systems. Contents Part I: Theory Chapter 1 First-Order Differential Equations Chapter 2 Linear Differential Systems Chapter 3 Second-Order Differential Equations Chapter 4 Nonlinear Differential Equations Chapter 5 Stability of Solutions Chapter 6 Differential Systems with Control Parameters Part II: Exercises Seminar 1 Classes of First-Order Differential Equations Seminar 2 Mathematical Modeling with Differential Equations Seminar 3 Linear Differential Systems Seminar 4 Second-Order Differential Equations Seminar 5 Gronwall’s Inequality Seminar 6 Method of Successive Approximations Seminar 7 Stability of Solutions Part III: Maple Code Lab 1 Introduction to Maple Lab 2 Differential Equations with Maple Lab 3 Linear Differential Systems Lab 4 Second-Order Differential Equations Lab 5 Nonlinear Differential Systems Lab 6 Numerical Computation of Solutions Lab 7 Writing Custom Maple Programs Lab 8 Differential Systems with Control Parameters
This book presents advanced studies on the conversion efficiency, mechanical reliability, and the quality of power related to wind energy systems. The main concern regarding such systems is reconciling the highly intermittent nature of the primary source (wind speed) with the demand for high-quality electrical energy and system stability. This means that wind energy conversion within the standard parameters imposed by the energy market and power industry is unachievable without optimization and control. The book discusses the rapid growth of control and optimization paradigms and applies them to wind energy systems: new controllers, new computational approaches, new applications, new algorithms, and new obstacles.
This volume presents a systematic and unified treatment of Leray-Schauder continuation theorems in nonlinear analysis. In particular, fixed point theory is established for many classes of maps, such as contractive, non-expansive, accretive, and compact maps, to name but a few. This book also presents coincidence and multiplicity results. Many appli
This introductory text combines models from physics and biology with rigorous reasoning in describing the theory of ordinary differential equations along with applications and computer simulations with Maple. Offering a concise course in the theory of ordinary differential equations, it also enables the reader to enter the field of computer simulations. Thus, it is a valuable read for students in mathematics as well as in physics and engineering. It is also addressed to all those interested in mathematical modeling with ordinary differential equations and systems. Contents Part I: Theory Chapter 1 First-Order Differential Equations Chapter 2 Linear Differential Systems Chapter 3 Second-Order Differential Equations Chapter 4 Nonlinear Differential Equations Chapter 5 Stability of Solutions Chapter 6 Differential Systems with Control Parameters Part II: Exercises Seminar 1 Classes of First-Order Differential Equations Seminar 2 Mathematical Modeling with Differential Equations Seminar 3 Linear Differential Systems Seminar 4 Second-Order Differential Equations Seminar 5 Gronwall’s Inequality Seminar 6 Method of Successive Approximations Seminar 7 Stability of Solutions Part III: Maple Code Lab 1 Introduction to Maple Lab 2 Differential Equations with Maple Lab 3 Linear Differential Systems Lab 4 Second-Order Differential Equations Lab 5 Nonlinear Differential Systems Lab 6 Numerical Computation of Solutions Lab 7 Writing Custom Maple Programs Lab 8 Differential Systems with Control Parameters
The text is intended for students who wish a concise and rapid introduction to some main topics in PDEs, necessary for understanding current research, especially in nonlinear PDEs. Organized on three parts, the book guides the reader from fundamental classical results, to some aspects of the modern theory and furthermore, to some techniques of nonlinear analysis. Compared to other introductory books in PDEs, this work clearly explains the transition from classical to generalized solutions and the natural way in which Sobolev spaces appear as completions of spaces of continuously differentiable functions with respect to energetic norms. Also, special attention is paid to the investigation of the solution operators associated to elliptic, parabolic and hyperbolic non-homogeneous equations anticipating the operator approach of nonlinear boundary value problems. Thus the reader is made to understand the role of linear theory for the analysis of nonlinear problems.
This book categorizes the wide area of data-driven model-free controllers, reveals the exact benefits of such controllers, gives the in-depth theory and mathematical proofs behind them, and finally discusses their applications. Each chapter includes a section for presenting the theory and mathematical definitions of one of the above mentioned algorithms. The second section of each chapter is dedicated to the examples and applications of the corresponding control algorithms in practical engineering problems. This book proposes to avoid complex mathematical equations, being generic as it includes several types of data-driven model-free controllers, such as Iterative Feedback Tuning controllers, Model-Free Controllers (intelligent PID controllers), Model-Free Adaptive Controllers, model-free sliding mode controllers, hybrid model‐free and model‐free adaptive‐Virtual Reference Feedback Tuning controllers, hybrid model-free and model-free adaptive fuzzy controllers and cooperative model-free controllers. The book includes the topic of optimal model-free controllers, as well. The optimal tuning of model-free controllers is treated in the chapters that deal with Iterative Feedback Tuning and Virtual Reference Feedback Tuning. Moreover, the extension of some model-free control algorithms to the consensus and formation-tracking problem of multi-agent dynamic systems is provided. This book can be considered as a textbook for undergraduate and postgraduate students, as well as a professional reference for industrial and academic researchers, attracting the readers from both industry and academia.
Nature-inspired Optimization Algorithms for Fuzzy Controlled Servo Systems explains fuzzy control in servo systems in a way that doesn't require any solid mathematical prerequisite. Analysis and design methodologies are covered, along with specific applications to servo systems and representative case studies. The theoretical approaches presented throughout the book are validated by the illustration of digital simulation and real-time experimental results. This book is a great resource for a wide variety of readers, including graduate students, engineers (designers, practitioners and researchers), and everyone who faces challenging control problems. Merges classical and modern approaches to fuzzy control Presents, in a unified structure, the essential aspects regarding fuzzy control in servo systems Explains notions of fuzzy set theory and fuzzy control to readers with limited experience
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