Analysis and Synthesis of Fuzzy Control Systems

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Author :
Publisher : CRC Press
ISBN 13 : 1420092650
Total Pages : 302 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Analysis and Synthesis of Fuzzy Control Systems by : Gang Feng

Download or read book Analysis and Synthesis of Fuzzy Control Systems written by Gang Feng and published by CRC Press. This book was released on 2018-09-03 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fuzzy logic control (FLC) has proven to be a popular control methodology for many complex systems in industry, and is often used with great success as an alternative to conventional control techniques. However, because it is fundamentally model free, conventional FLC suffers from a lack of tools for systematic stability analysis and controller design. To address this problem, many model-based fuzzy control approaches have been developed, with the fuzzy dynamic model or the Takagi and Sugeno (T–S) fuzzy model-based approaches receiving the greatest attention. Analysis and Synthesis of Fuzzy Control Systems: A Model-Based Approach offers a unique reference devoted to the systematic analysis and synthesis of model-based fuzzy control systems. After giving a brief review of the varieties of FLC, including the T–S fuzzy model-based control, it fully explains the fundamental concepts of fuzzy sets, fuzzy logic, and fuzzy systems. This enables the book to be self-contained and provides a basis for later chapters, which cover: T–S fuzzy modeling and identification via nonlinear models or data Stability analysis of T–S fuzzy systems Stabilization controller synthesis as well as robust H∞ and observer and output feedback controller synthesis Robust controller synthesis of uncertain T–S fuzzy systems Time-delay T–S fuzzy systems Fuzzy model predictive control Robust fuzzy filtering Adaptive control of T–S fuzzy systems A reference for scientists and engineers in systems and control, the book also serves the needs of graduate students exploring fuzzy logic control. It readily demonstrates that conventional control technology and fuzzy logic control can be elegantly combined and further developed so that disadvantages of conventional FLC can be avoided and the horizon of conventional control technology greatly extended. Many chapters feature application simulation examples and practical numerical examples based on MATLAB®.

Fuzzy Control

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Author :
Publisher : John Wiley & Sons
ISBN 13 :
Total Pages : 424 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Fuzzy Control by : Shehu S. Farinwata

Download or read book Fuzzy Control written by Shehu S. Farinwata and published by John Wiley & Sons. This book was released on 2000-06-08 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fuzzy Control Synthesis and Analysis Edited by Shehu S. Farinwata Ford Motor Company, Research Laboratory, Dearborn, Michigan, USA Dimitar Filev Ford Motor Company, AMTDC, Redford, Michigan, USA Reza Langari Texas A & M University, College Station, Texas, USA Fuzzy techniques are used to cope with imprecision in the basic elements of a process under control. Written by an international team of researchers this edited volume covers the modeling, analysis and synthesis of fuzzy control systems. Features include: ? Comprehensive coverage of fuzzy dynamical systems, robustness, stability and sensitivity -- giving the reader a good grasp of the fundamentals of fuzzy control ? Focus on the analytical structures of new fuzzy modeling approaches based on the Takagi-Sugeno-Kang (TSK) or Takagi-Sugeno (TS) model ? Applications of fuzzy control to aircraft systems, rocket engines and automotive engines ? Problems and examples illustrating how fuzzy approaches may be applied to the modeling, analysis and synthesis of closed-loop systems Design and control engineers will value the advanced control techniques and new design and analysis tools presented. Postgraduates studying fuzzy control will find this book a useful reference on synthesis, systems analysis and advanced nonlinear control methods.

Fuzzy Systems

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Publisher : Springer Science & Business Media
ISBN 13 : 1461555051
Total Pages : 532 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis Fuzzy Systems by : Hung T. Nguyen

Download or read book Fuzzy Systems written by Hung T. Nguyen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: The analysis and control of complex systems have been the main motivation for the emergence of fuzzy set theory since its inception. It is also a major research field where many applications, especially industrial ones, have made fuzzy logic famous. This unique handbook is devoted to an extensive, organized, and up-to-date presentation of fuzzy systems engineering methods. The book includes detailed material and extensive bibliographies, written by leading experts in the field, on topics such as: Use of fuzzy logic in various control systems. Fuzzy rule-based modeling and its universal approximation properties. Learning and tuning techniques for fuzzy models, using neural networks and genetic algorithms. Fuzzy control methods, including issues such as stability analysis and design techniques, as well as the relationship with traditional linear control. Fuzzy sets relation to the study of chaotic systems, and the fuzzy extension of set-valued approaches to systems modeling through the use of differential inclusions. Fuzzy Systems: Modeling and Control is part of The Handbooks of Fuzzy Sets Series. The series provides a complete picture of contemporary fuzzy set theory and its applications. This volume is a key reference for systems engineers and scientists seeking a guide to the vast amount of literature in fuzzy logic modeling and control.

Advanced Control Systems

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Publisher : CRC Press
ISBN 13 : 1000794067
Total Pages : 476 pages
Book Rating : 4.0/5 (7 download)

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Book Synopsis Advanced Control Systems by : Yuriy P. Kondratenko

Download or read book Advanced Control Systems written by Yuriy P. Kondratenko and published by CRC Press. This book was released on 2022-09-01 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced Control Systems: Theory and Applications provides an overview of advanced research lines in control systems as well as in design, development and implementation methodologies for perspective control systems and their components in different areas of industrial and special applications. It consists of extended versions of the selected papers presented at the XXV International Conference on Automatic Control “Automatics 2018” (September 18-19, 2018, Lviv, Ukraine) which is the main Ukrainian Control Conference organized by Ukrainian Association on Automatic Control (National member organization of IFAC) and Lviv National University “Lvivska Politechnica”. More than 100 papers were presented at the conference with topics including: mathematical problems of control, optimization and game theory; control and identification under uncertainty; automated control of technical, technological and biotechnical objects; controlling the aerospace craft, marine vessels and other moving objects; intelligent control and information processing; mechatronics and robotics; information measuring technologies in automation; automation and IT training of personnel; the Internet of things and the latest technologies. The book is divided into two main parts, the first concerning theory (7 chapters) and the second concerning applications (7 chapters) of advanced control systems. The first part “Advances in Theoretical Research on Automatic Control” consists of theoretical research results which deal with descriptor control impulsive delay systems, motion control in condition of conflict, inverse dynamic models, invariant relations in optimal control, robust adaptive control, bio-inspired algorithms, optimization of fuzzy control systems, and extremal routing problem with constraints and complicated cost functions. The second part “Advances in Control Systems Applications” is based on the chapters which consider different aspects of practical implementation of advanced control systems, in particular, special cases in determining the spacecraft position and attitude using computer vision system, the spacecraft orientation by information from a system of stellar sensors, control synthesis of rotational and spatial spacecraft motion at approaching stage of docking, intelligent algorithms for the automation of complex biotechnical objects, an automatic control system for the slow pyrolysis of organic substances with variable composition, simulation complex of hierarchical systems based on the foresight and cognitive modelling, and advanced identification of impulse processes in cognitive maps. The chapters have been structured to provide an easy-to-follow introduction to the topics that are addressed, including the most relevant references, so that anyone interested in this field can get started in the area. This book may be useful for researchers and students who are interesting in advanced control systems.

Fuzzy Control Systems Design and Analysis

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Publisher : John Wiley & Sons
ISBN 13 : 0471465224
Total Pages : 321 pages
Book Rating : 4.4/5 (714 download)

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Book Synopsis Fuzzy Control Systems Design and Analysis by : Kazuo Tanaka

Download or read book Fuzzy Control Systems Design and Analysis written by Kazuo Tanaka and published by John Wiley & Sons. This book was released on 2004-04-07 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive treatment of model-based fuzzy control systems This volume offers full coverage of the systematic framework for the stability and design of nonlinear fuzzy control systems. Building on the Takagi-Sugeno fuzzy model, authors Tanaka and Wang address a number of important issues in fuzzy control systems, including stability analysis, systematic design procedures, incorporation of performance specifications, numerical implementations, and practical applications. Issues that have not been fully treated in existing texts, such as stability analysis, systematic design, and performance analysis, are crucial to the validity and applicability of fuzzy control methodology. Fuzzy Control Systems Design and Analysis addresses these issues in the framework of parallel distributed compensation, a controller structure devised in accordance with the fuzzy model. This balanced treatment features an overview of fuzzy control, modeling, and stability analysis, as well as a section on the use of linear matrix inequalities (LMI) as an approach to fuzzy design and control. It also covers advanced topics in model-based fuzzy control systems, including modeling and control of chaotic systems. Later sections offer practical examples in the form of detailed theoretical and experimental studies of fuzzy control in robotic systems and a discussion of future directions in the field. Fuzzy Control Systems Design and Analysis offers an advanced treatment of fuzzy control that makes a useful reference for researchers and a reliable text for advanced graduate students in the field.

Fuzzy Logic Control

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Author :
Publisher : World Scientific
ISBN 13 : 9789810238254
Total Pages : 344 pages
Book Rating : 4.2/5 (382 download)

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Book Synopsis Fuzzy Logic Control by : H. B. Verbruggen

Download or read book Fuzzy Logic Control written by H. B. Verbruggen and published by World Scientific. This book was released on 1999 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fuzzy logic control has become an important methodology in control engineering. This volume deals with applications of fuzzy logic control in various domains. The contributions are divided into three parts. The first part consists of two state-of-the-art tutorials on fuzzy control and fuzzy modeling. Surveys of advanced methodologies are included in the second part. These surveys address fuzzy decision making and control, fault detection, isolation and diagnosis, complexity reduction in fuzzy systems and neuro-fuzzy methods. The third part contains application-oriented contributions from various fields, such as process industry, cement and ceramics, vehicle control and traffic management, electromechanical and production systems, avionics, biotechnology and medical applications. The book is intended for researchers both from the academic world and from industry.

Fuzzy Control and Identification

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Author :
Publisher : John Wiley & Sons
ISBN 13 : 1118097815
Total Pages : 199 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Fuzzy Control and Identification by : John H. Lilly

Download or read book Fuzzy Control and Identification written by John H. Lilly and published by John Wiley & Sons. This book was released on 2011-03-10 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an introduction to basic fuzzy logic and Mamdani and Takagi-Sugeno fuzzy systems. The text shows how these can be used to control complex nonlinear engineering systems, while also also suggesting several approaches to modeling of complex engineering systems with unknown models. Finally, fuzzy modeling and control methods are combined in the book, to create adaptive fuzzy controllers, ending with an example of an obstacle-avoidance controller for an autonomous vehicle using modus ponendo tollens logic.

Introduction to Fuzzy Sets, Fuzzy Logic, and Fuzzy Control Systems

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Author :
Publisher : CRC Press
ISBN 13 : 1420039814
Total Pages : 329 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Introduction to Fuzzy Sets, Fuzzy Logic, and Fuzzy Control Systems by : Guanrong Chen

Download or read book Introduction to Fuzzy Sets, Fuzzy Logic, and Fuzzy Control Systems written by Guanrong Chen and published by CRC Press. This book was released on 2000-11-27 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the early 1970s, fuzzy systems and fuzzy control theories added a new dimension to control systems engineering. From its beginnings as mostly heuristic and somewhat ad hoc, more recent and rigorous approaches to fuzzy control theory have helped make it an integral part of modern control theory and produced many exciting results. Yesterday's "art

New Approaches to Fuzzy Modeling and Control

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Author :
Publisher : World Scientific
ISBN 13 : 9789810243340
Total Pages : 204 pages
Book Rating : 4.2/5 (433 download)

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Book Synopsis New Approaches to Fuzzy Modeling and Control by : Michael Margaliot

Download or read book New Approaches to Fuzzy Modeling and Control written by Michael Margaliot and published by World Scientific. This book was released on 2000 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fuzzy logic has found applications in an incredibly wide range of areas in the relatively wide range of areas in the relatively short time since its conception. It was invented by Lotfi Zadeh, a leading systems expert, so it is perhaps not surprising that system theory is one of the areas in which fuzzy logic has made a profound impact. Fuzzy logic combined with the paradigm of computing with words allows the use and manipulation of human knowledge and reasoning in the modeling and control of dynamical systems. This monograph presents new approaches to the construction of fuzzy models and to the design of fuzzy controllers. The emphasis is on developing methods that allow systematic design on the one hand and mathematical analysis of the resulting system on the other. In particular, the methods described allow rigorous analysis of the stability and robustness of the systems, which are crucial issues in control theory. The first theme of the book is a new approach to the system design and analysis of fuzzy controllers, given linguistic information concerning the plant and the control objective. The new approach, fuzzy Lyapunov synthesis, is a computing-with-words version of the well-known (classical) Lyapunov synthesis method. The second theme of the book is to show that fuzzy controllers are in fact solutions to a nonlinear optimal control problem. The authors formulate a novel nonlinear optimal control problem, consisting of a new state-space model -- referred to as the hyperbolic state-space model -- and a new cost functional and show that its solution is a fuzzy controller. This leads to a new framework for fuzzy modeling and control that combines the advantages of the fuzzyworld, such as linguistic interpretability, and of classical optimal control theory, such as guaranteed stability and robustness.

An Introduction to Fuzzy Logic Applications in Intelligent Systems

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Author :
Publisher : Springer Science & Business Media
ISBN 13 : 1461536405
Total Pages : 358 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis An Introduction to Fuzzy Logic Applications in Intelligent Systems by : Ronald R. Yager

Download or read book An Introduction to Fuzzy Logic Applications in Intelligent Systems written by Ronald R. Yager and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to Fuzzy Logic Applications in Intelligent Systems consists of a collection of chapters written by leading experts in the field of fuzzy sets. Each chapter addresses an area where fuzzy sets have been applied to situations broadly related to intelligent systems. The volume provides an introduction to and an overview of recent applications of fuzzy sets to various areas of intelligent systems. Its purpose is to provide information and easy access for people new to the field. The book also serves as an excellent reference for researchers in the field and those working in the specifics of systems development. People in computer science, especially those in artificial intelligence, knowledge-based systems, and intelligent systems will find this to be a valuable sourcebook. Engineers, particularly control engineers, will also have a strong interest in this book. Finally, the book will be of interest to researchers working in decision support systems, operations research, decision theory, management science and applied mathematics. An Introduction to Fuzzy Logic Applications in Intelligent Systems may also be used as an introductory text and, as such, it is tutorial in nature.

Fuzzy Control

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Author :
Publisher : Prentice Hall
ISBN 13 :
Total Pages : 506 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Fuzzy Control by : Kevin M. Passino

Download or read book Fuzzy Control written by Kevin M. Passino and published by Prentice Hall. This book was released on 1998 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction; Fuzzy control: the basics; Case studies in design and implementation; nonlinear analysis; Fuzzy identification and estimation; Adaptive fuzzy control; Fuzzy supervisory control; Perspectives on fuzzy control.

Fuzzy Sets, Fuzzy Logic, And Fuzzy Systems: Selected Papers By Lotfi A Zadeh

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Publisher : World Scientific
ISBN 13 : 9814499811
Total Pages : 842 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Fuzzy Sets, Fuzzy Logic, And Fuzzy Systems: Selected Papers By Lotfi A Zadeh by : George J Klir

Download or read book Fuzzy Sets, Fuzzy Logic, And Fuzzy Systems: Selected Papers By Lotfi A Zadeh written by George J Klir and published by World Scientific. This book was released on 1996-05-30 with total page 842 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of selected papers written by the founder of fuzzy set theory, Lotfi A Zadeh. Since Zadeh is not only the founder of this field, but has also been the principal contributor to its development over the last 30 years, the papers contain virtually all the major ideas in fuzzy set theory, fuzzy logic, and fuzzy systems in their historical context. Many of the ideas presented in the papers are still open to further development. The book is thus an important resource for anyone interested in the areas of fuzzy set theory, fuzzy logic, and fuzzy systems, as well as their applications. Moreover, the book is also intended to play a useful role in higher education, as a rich source of supplementary reading in relevant courses and seminars.The book contains a bibliography of all papers published by Zadeh in the period 1949-1995. It also contains an introduction that traces the development of Zadeh's ideas pertaining to fuzzy sets, fuzzy logic, and fuzzy systems via his papers. The ideas range from his 1965 seminal idea of the concept of a fuzzy set to ideas reflecting his current interest in computing with words — a computing in which linguistic expressions are used in place of numbers.Places in the papers, where each idea is presented can easily be found by the reader via the Subject Index.

Analysis and Synthesis of Fuzzy Control Systems

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Author :
Publisher :
ISBN 13 : 9781351825696
Total Pages : pages
Book Rating : 4.8/5 (256 download)

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Book Synopsis Analysis and Synthesis of Fuzzy Control Systems by : Gang Feng

Download or read book Analysis and Synthesis of Fuzzy Control Systems written by Gang Feng and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "Fuzzy logic control (FLC) has proven to be a popular control methodology for many complex systems in industry, and is often used with great success as an alternative to conventional control techniques. However, because it is fundamentally model free, conventional FLC suffers from a lack of tools for systematic stability analysis and controller design. To address this problem, many model-based fuzzy control approaches have been developed, with the fuzzy dynamic model or the Takagi and Sugeno (T-S) fuzzy model-based approaches receiving the greatest attention. Analysis and Synthesis of Fuzzy Control Systems: A Model-Based Approach offers a unique reference devoted to the systematic analysis and synthesis of model-based fuzzy control systems. After giving a brief review of the varieties of FLC, including the T-S fuzzy model-based control, it fully explains the fundamental concepts of fuzzy sets, fuzzy logic, and fuzzy systems. This enables the book to be self-contained and provides a basis for later chapters, which cover:T-S fuzzy modeling and identification via nonlinear models or data Stability analysis of T-S fuzzy systems Stabilization controller synthesis as well as robust H? and observer and output feedback controller synthesis Robust controller synthesis of uncertain T-S fuzzy systemsTime-delay T-S fuzzy systems Fuzzy model predictive control Robust fuzzy filteringAdaptive control of T-S fuzzy systems A reference for scientists and engineers in systems and control, the book also serves the needs of graduate students exploring fuzzy logic control. It readily demonstrates that conventional control technology and fuzzy logic control can be elegantly combined and further developed so that disadvantages of conventional FLC can be avoided and the horizon of conventional control technology greatly extended. Many chapters feature application simulation examples and practical numerical examples based on MATLAB®."--Provided by publisher.

Fuzzy System Identification and Adaptive Control

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Author :
Publisher : Springer
ISBN 13 : 3030198820
Total Pages : 293 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Fuzzy System Identification and Adaptive Control by : Ruiyun Qi

Download or read book Fuzzy System Identification and Adaptive Control written by Ruiyun Qi and published by Springer. This book was released on 2019-06-11 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides readers with a systematic and unified framework for identification and adaptive control of Takagi–Sugeno (T–S) fuzzy systems. Its design techniques help readers applying these powerful tools to solve challenging nonlinear control problems. The book embodies a systematic study of fuzzy system identification and control problems, using T–S fuzzy system tools for both function approximation and feedback control of nonlinear systems. Alongside this framework, the book also: introduces basic concepts of fuzzy sets, logic and inference system; discusses important properties of T–S fuzzy systems; develops offline and online identification algorithms for T–S fuzzy systems; investigates the various controller structures and corresponding design conditions for adaptive control of continuous-time T–S fuzzy systems; develops adaptive control algorithms for discrete-time input–output form T–S fuzzy systems with much relaxed design conditions, and discrete-time state-space T–S fuzzy systems; and designs stable parameter-adaptation algorithms for both linearly and nonlinearly parameterized T–S fuzzy systems. The authors address adaptive fault compensation problems for T–S fuzzy systems subject to actuator faults. They cover a broad spectrum of related technical topics and to develop a substantial set of adaptive nonlinear system control tools. Fuzzy System Identification and Adaptive Control helps engineers in the mechanical, electrical and aerospace fields, to solve complex control design problems. The book can be used as a reference for researchers and academics in nonlinear, intelligent, adaptive and fault-tolerant control.

Analysis and Synthesis for Interval Type-2 Fuzzy-Model-Based Systems

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Author :
Publisher : Springer
ISBN 13 : 9811005931
Total Pages : 263 pages
Book Rating : 4.8/5 (11 download)

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Book Synopsis Analysis and Synthesis for Interval Type-2 Fuzzy-Model-Based Systems by : Hongyi Li

Download or read book Analysis and Synthesis for Interval Type-2 Fuzzy-Model-Based Systems written by Hongyi Li and published by Springer. This book was released on 2016-02-29 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops a set of reference methods capable of modeling uncertainties existing in membership functions, and analyzing and synthesizing the interval type-2 fuzzy systems with desired performances. It also provides numerous simulation results for various examples, which fill certain gaps in this area of research and may serve as benchmark solutions for the readers. Interval type-2 T-S fuzzy models provide a convenient and flexible method for analysis and synthesis of complex nonlinear systems with uncertainties.

Fuzzy Control

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Publisher : Springer Science & Business Media
ISBN 13 : 3790818410
Total Pages : 413 pages
Book Rating : 4.7/5 (98 download)

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Book Synopsis Fuzzy Control by : Rainer Hampel

Download or read book Fuzzy Control written by Rainer Hampel and published by Springer Science & Business Media. This book was released on 2013-06-02 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present edited volume is of special importance, and for various reasons. First of all, it is one of the most comprehensive and multifaceted coverage of broadly per ceived fuzzy control in the literature. The editors have succeeded to collect papers from leading scholars and researchers on various subjects related to the topic of the volume. What is relevant and original is that - as opposed to so many volumes on fuzzy control published by virtually all major publishing houses that are strongly technically oriented and covering a narrow spectrum of issues relevant to fuzzy con trol itself - the editors have adopted a more general and far sighted approach. Basically, the perspective assumed in the volume is that though fuzzy control has reached such a level of maturity and implementability that it has become a part of in dustrial practice, science and academic research still have a relevant role to play in this area. One should however take into account that by their very nature, the role of science and academic research is very peculiar and going beyond straightforward ap plications, ad hoc solutions, "quick and dirty" tools and techniques, etc. that are usu ally effective and efficient for solving practical problems. This does not mean that as pects of practical implementations should not be accounted for by scholars and re searchers.

Feedback Control Theory

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Author :
Publisher : Courier Corporation
ISBN 13 : 0486318338
Total Pages : 264 pages
Book Rating : 4.4/5 (863 download)

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Book Synopsis Feedback Control Theory by : John C. Doyle

Download or read book Feedback Control Theory written by John C. Doyle and published by Courier Corporation. This book was released on 2013-04-09 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: An excellent introduction to feedback control system design, this book offers a theoretical approach that captures the essential issues and can be applied to a wide range of practical problems. Its explorations of recent developments in the field emphasize the relationship of new procedures to classical control theory, with a focus on single input and output systems that keeps concepts accessible to students with limited backgrounds. The text is geared toward a single-semester senior course or a graduate-level class for students of electrical engineering. The opening chapters constitute a basic treatment of feedback design. Topics include a detailed formulation of the control design program, the fundamental issue of performance/stability robustness tradeoff, and the graphical design technique of loopshaping. Subsequent chapters extend the discussion of the loopshaping technique and connect it with notions of optimality. Concluding chapters examine controller design via optimization, offering a mathematical approach that is useful for multivariable systems.