Fractional Order Nonlinear Systems

Author : Ivo Petráš
Publisher : Springer Science & Business Media
Page : 218 pages
File Size : 51,7 Mb
Release : 2011-05-30
Category : Technology & Engineering
ISBN : 9783642181016

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Fractional-Order Nonlinear Systems by Ivo Petráš Pdf

"Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation" presents a study of fractional-order chaotic systems accompanied by Matlab programs for simulating their state space trajectories, which are shown in the illustrations in the book. Description of the chaotic systems is clearly presented and their analysis and numerical solution are done in an easy-to-follow manner. Simulink models for the selected fractional-order systems are also presented. The readers will understand the fundamentals of the fractional calculus, how real dynamical systems can be described using fractional derivatives and fractional differential equations, how such equations can be solved, and how to simulate and explore chaotic systems of fractional order. The book addresses to mathematicians, physicists, engineers, and other scientists interested in chaos phenomena or in fractional-order systems. It can be used in courses on dynamical systems, control theory, and applied mathematics at graduate or postgraduate level. Ivo Petráš is an Associate Professor of automatic control and the Director of the Institute of Control and Informatization of Production Processes, Faculty of BERG, Technical University of Košice, Slovak Republic. His main research interests include control systems, industrial automation, and applied mathematics.

Author : Omar Naifar,Abdellatif Ben Makhlouf
Publisher : Springer Nature
Page : 224 pages
File Size : 55,8 Mb
Release : 2021-08-30
Category : Technology & Engineering
ISBN : 9783030714468

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Fractional Order Systems—Control Theory and Applications by Omar Naifar,Abdellatif Ben Makhlouf Pdf

This book aims to bring together the latest innovative knowledge, analysis, and synthesis of fractional control problems of nonlinear systems as well as some related applications. Fractional order systems (FOS) are dynamical systems that can be modelled by a fractional differential equation carried with a non-integer derivative. In the last few decades, the growth of science and engineering systems has considerably stimulated the employment of fractional calculus in many subjects of control theory, for example, in stability, stabilization, controllability, observability, observer design, and fault estimation. The application of control theory in FOS is an important issue in many engineering applications. So, to accurately describe these systems, the fractional order differential equations have been introduced.

Author : Mou Chen,Shuyi Shao,Peng Shi
Publisher : John Wiley & Sons
Page : 252 pages
File Size : 43,5 Mb
Release : 2017-12-26
Category : Technology & Engineering
ISBN : 9781119393276

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Robust Adaptive Control for Fractional-Order Systems with Disturbance and Saturation by Mou Chen,Shuyi Shao,Peng Shi Pdf

A treatise on investigating tracking control and synchronization control of fractional-order nonlinear systems with system uncertainties, external disturbance, and input saturation Robust Adaptive Control for Fractional-Order Systems, with Disturbance and Saturation provides the reader with a good understanding on how to achieve tracking control and synchronization control of fractional-order nonlinear systems with system uncertainties, external disturbance, and input saturation. Although some texts have touched upon control of fractional-order systems, the issues of input saturation and disturbances have rarely been considered together. This book offers chapter coverage of fractional calculus and fractional-order systems; fractional-order PID controller and fractional-order disturbance observer; design of fractional-order controllers for nonlinear chaotic systems and some applications; sliding mode control for fractional-order nonlinear systems based on disturbance observer; disturbance observer based neural control for an uncertain fractional-order rotational mechanical system; adaptive neural tracking control for uncertain fractional-order chaotic systems subject to input saturation and disturbance; stabilization control of continuous-time fractional positive systems based on disturbance observer; sliding mode synchronization control for fractional-order chaotic systems with disturbance; and more. Based on the approximation ability of the neural network (NN), the adaptive neural control schemes are reported for uncertain fractional-order nonlinear systems Covers the disturbance estimation techniques that have been developed to alleviate the restriction faced by traditional feedforward control and reject the effect of external disturbances for uncertain fractional-order nonlinear systems By combining the NN with the disturbance observer, the disturbance observer based adaptive neural control schemes have been studied for uncertain fractional-order nonlinear systems with unknown disturbances Considers, together, the issue of input saturation and the disturbance for the control of fractional-order nonlinear systems in the present of system uncertainty, external disturbance, and input saturation Robust Adaptive Control for Fractional-Order Systems, with Disturbance and Saturation can be used as a reference for the academic research on fractional-order nonlinear systems or used in Ph.D. study of control theory and engineering.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 53,6 Mb
Release : 2024-06-03
Category : Electronic
ISBN : 9789814465151

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Fractional Order Systems by Anonim Pdf

Author : Omar Naifar,Abdellatif Ben Makhlouf
Publisher : Unknown
Page : 0 pages
File Size : 44,5 Mb
Release : 2022
Category : Electronic
ISBN : 3030714470

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Fractional Order Systems-Control Theory and Applications by Omar Naifar,Abdellatif Ben Makhlouf Pdf

This book aims to bring together the latest innovative knowledge, analysis, and synthesis of fractional control problems of nonlinear systems as well as some related applications. Fractional order systems (FOS) are dynamical systems that can be modelled by a fractional differential equation carried with a non-integer derivative. In the last few decades, the growth of science and engineering systems has considerably stimulated the employment of fractional calculus in many subjects of control theory, for example, in stability, stabilization, controllability, observability, observer design, and fault estimation. The application of control theory in FOS is an important issue in many engineering applications. So, to accurately describe these systems, the fractional order differential equations have been introduced.

Author : Rafael Martínez-Guerra,Claudia Alejandra Pérez-Pinacho
Publisher : Springer
Page : 185 pages
File Size : 48,8 Mb
Release : 2018-07-23
Category : Science
ISBN : 9783319939469

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Advances in Synchronization of Coupled Fractional Order Systems by Rafael Martínez-Guerra,Claudia Alejandra Pérez-Pinacho Pdf

After a short introduction to the fundamentals, this book provides a detailed account of major advances in applying fractional calculus to dynamical systems. Fractional order dynamical systems currently continue to gain further importance in many areas of science and engineering. As with many other approaches to mathematical modeling, the first issue to be addressed is the need to couple a definition of the fractional differentiation or integration operator with the types of dynamical systems that are analyzed. As such, for the fundamentals the focus is on basic aspects of fractional calculus, in particular stability analysis, which is required to tackle synchronization in coupled fractional order systems, to understand the essence of estimators for related integer order systems, and to keep track of the interplay between synchronization and parameter observation. This serves as the common basis for the more advanced topics and applications presented in the subsequent chapters, which include an introduction to the 'Immersion and Invariance' (I&I) methodology, the masterslave synchronization scheme for partially known nonlinear fractional order systems, Fractional Algebraic Observability (FAO) and Fractional Generalized quasi-Synchronization (FGqS) to name but a few. This book is intended not only for applied mathematicians and theoretical physicists, but also for anyone in applied science dealing with complex nonlinear systems.

Author : Riccardo Caponetto
Publisher : World Scientific
Page : 201 pages
File Size : 43,9 Mb
Release : 2010
Category : Computers
ISBN : 9789814304207

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Fractional Order Systems by Riccardo Caponetto Pdf

This book aims to propose implementations and applications of Fractional Order Systems (FOS). It is well known that FOS can be applied in control applications and systems modeling, and their effectiveness has been proven in many theoretical works and simulation routines. A further and mandatory step for FOS real world utilization is their hardware implementation and applications on real systems modeling. With this viewpoint, introductive chapters on FOS are included, on the definition of stability region of Fractional Order PID Controller and Chaotic FOS, followed by the practical implementation based on Microcontroller, Field Programmable Gate Array, Field Programmable Analog Array and Switched Capacitor. Another section is dedicated to FO modeling of Ionic Polymeric Metal Composite (IPMC). This new material may have applications in robotics, aerospace and biomedicine.

Author : Dumitru Baleanu,José António Tenreiro Machado,Albert C. J. Luo
Publisher : Springer Science & Business Media
Page : 310 pages
File Size : 55,5 Mb
Release : 2011-11-19
Category : Technology & Engineering
ISBN : 1461404576

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Fractional Dynamics and Control by Dumitru Baleanu,José António Tenreiro Machado,Albert C. J. Luo Pdf

Fractional Dynamics and Control provides a comprehensive overview of recent advances in the areas of nonlinear dynamics, vibration and control with analytical, numerical, and experimental results. This book provides an overview of recent discoveries in fractional control, delves into fractional variational principles and differential equations, and applies advanced techniques in fractional calculus to solving complicated mathematical and physical problems.Finally, this book also discusses the role that fractional order modeling can play in complex systems for engineering and science.

Author : Ahmad Taher Azar,Ahmed G. Radwan,Sundarapandian Vaidyanathan
Publisher : Academic Press
Page : 741 pages
File Size : 45,6 Mb
Release : 2018-08-16
Category : Technology & Engineering
ISBN : 9780128163085

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Fractional Order Systems by Ahmad Taher Azar,Ahmed G. Radwan,Sundarapandian Vaidyanathan Pdf

Fractional Order Systems: Optimization, Control, Circuit Realizations and Applications consists of 21 contributed chapters by subject experts. Chapters offer practical solutions and novel methods for recent research problems in the multidisciplinary applications of fractional order systems, such as FPGA, circuits, memristors, control algorithms, photovoltaic systems, robot manipulators, oscillators, etc. This book is ideal for researchers working in the modeling and applications of both continuous-time and discrete-time dynamics and chaotic systems. Researchers from academia and industry who are working in research areas such as control engineering, electrical engineering, mechanical engineering, computer science, and information technology will find the book most informative. Discusses multi-disciplinary applications with new fundamentals, modeling, analysis, design, realization and experimental results Includes new circuits and systems based on the new nonlinear elements Covers most of the linear and nonlinear fractional-order theorems that will solve many scientific issues for researchers Closes the gap between theoretical approaches and real-world applications Provides MATLAB® and Simulink code for many of the applications in the book

Author : Francesco Amato,Gianmaria De Tommasi,Alfredo Pironti
Publisher : John Wiley & Sons
Page : 184 pages
File Size : 51,8 Mb
Release : 2018-10-08
Category : Technology & Engineering
ISBN : 9781119140528

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Finite-Time Stability: An Input-Output Approach by Francesco Amato,Gianmaria De Tommasi,Alfredo Pironti Pdf

Systematically presents the input-output finite-time stability (IO-FTS) analysis of dynamical systems, covering issues of analysis, design and robustness The interest in finite-time control has continuously grown in the last fifteen years. This book systematically presents the input-output finite-time stability (IO-FTS) analysis of dynamical systems, with specific reference to linear time-varying systems and hybrid systems. It discusses analysis, design and robustness issues, and includes applications to real world engineering problems. While classical FTS has an important theoretical significance, IO-FTS is a more practical concept, which is more suitable for real engineering applications, the goal of the research on this topic in the coming years. Key features: Includes applications to real world engineering problems. Input-output finite-time stability (IO-FTS) is a practical concept, useful to study the behavior of a dynamical system within a finite interval of time. Computationally tractable conditions are provided that render the technique applicable to time-invariant as well as time varying and impulsive (i.e. switching) systems. The LMIs formulation allows mixing the IO-FTS approach with existing control techniques (e. g. H∞ control, optimal control, pole placement, etc.). This book is essential reading for university researchers as well as post-graduate engineers practicing in the field of robust process control in research centers and industries. Topics dealt with in the book could also be taught at the level of advanced control courses for graduate students in the department of electrical and computer engineering, mechanical engineering, aeronautics and astronautics, and applied mathematics.

Author : Ahmad Taher Azar,Sundarapandian Vaidyanathan,Adel Ouannas
Publisher : Springer
Page : 877 pages
File Size : 44,7 Mb
Release : 2017-02-27
Category : Technology & Engineering
ISBN : 9783319502496

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Fractional Order Control and Synchronization of Chaotic Systems by Ahmad Taher Azar,Sundarapandian Vaidyanathan,Adel Ouannas Pdf

The book reports on the latest advances in and applications of fractional order control and synchronization of chaotic systems, explaining the concepts involved in a clear, matter-of-fact style. It consists of 30 original contributions written by eminent scientists and active researchers in the field that address theories, methods and applications in a number of research areas related to fractional order control and synchronization of chaotic systems, such as: fractional chaotic systems, hyperchaotic systems, complex systems, fractional order discrete chaotic systems, chaos control, chaos synchronization, jerk circuits, fractional chaotic systems with hidden attractors, neural network, fuzzy logic controllers, behavioral modeling, robust and adaptive control, sliding mode control, different types of synchronization, circuit realization of chaotic systems, etc. In addition to providing readers extensive information on chaos fundamentals, fractional calculus, fractional differential equations, fractional control and stability, the book also discusses key applications of fractional order chaotic systems, as well as multidisciplinary solutions developed via control modeling. As such, it offers the perfect reference guide for graduate students, researchers and practitioners in the areas of fractional order control systems and fractional order chaotic systems.

Author : Mou Chen,Shuyi Shao,Peng Shi
Publisher : John Wiley & Sons
Page : 256 pages
File Size : 42,7 Mb
Release : 2017-10-20
Category : Technology & Engineering
ISBN : 9781119393337

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Robust Adaptive Control for Fractional-Order Systems with Disturbance and Saturation by Mou Chen,Shuyi Shao,Peng Shi Pdf

A treatise on investigating tracking control and synchronization control of fractional-order nonlinear systems with system uncertainties, external disturbance, and input saturation Robust Adaptive Control for Fractional-Order Systems, with Disturbance and Saturation provides the reader with a good understanding on how to achieve tracking control and synchronization control of fractional-order nonlinear systems with system uncertainties, external disturbance, and input saturation. Although some texts have touched upon control of fractional-order systems, the issues of input saturation and disturbances have rarely been considered together. This book offers chapter coverage of fractional calculus and fractional-order systems; fractional-order PID controller and fractional-order disturbance observer; design of fractional-order controllers for nonlinear chaotic systems and some applications; sliding mode control for fractional-order nonlinear systems based on disturbance observer; disturbance observer based neural control for an uncertain fractional-order rotational mechanical system; adaptive neural tracking control for uncertain fractional-order chaotic systems subject to input saturation and disturbance; stabilization control of continuous-time fractional positive systems based on disturbance observer; sliding mode synchronization control for fractional-order chaotic systems with disturbance; and more. Based on the approximation ability of the neural network (NN), the adaptive neural control schemes are reported for uncertain fractional-order nonlinear systems Covers the disturbance estimation techniques that have been developed to alleviate the restriction faced by traditional feedforward control and reject the effect of external disturbances for uncertain fractional-order nonlinear systems By combining the NN with the disturbance observer, the disturbance observer based adaptive neural control schemes have been studied for uncertain fractional-order nonlinear systems with unknown disturbances Considers, together, the issue of input saturation and the disturbance for the control of fractional-order nonlinear systems in the present of system uncertainty, external disturbance, and input saturation Robust Adaptive Control for Fractional-Order Systems, with Disturbance and Saturation can be used as a reference for the academic research on fractional-order nonlinear systems or used in Ph.D. study of control theory and engineering.

Author : Jean-Claude Trigeassou,Nezha Maamri
Publisher : John Wiley & Sons
Page : 426 pages
File Size : 50,7 Mb
Release : 2020-02-26
Category : Technology & Engineering
ISBN : 9781786304551

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Analysis, Modeling and Stability of Fractional Order Differential Systems 2 by Jean-Claude Trigeassou,Nezha Maamri Pdf

This book introduces an original fractional calculus methodology (the infinite state approach) which is applied to the modeling of fractional order differential equations (FDEs) and systems (FDSs). Its modeling is based on the frequency distributed fractional integrator, while the resulting model corresponds to an integer order and infinite dimension state space representation. This original modeling allows the theoretical concepts of integer order systems to be generalized to fractional systems, with a particular emphasis on a convolution formulation. With this approach, fundamental issues such as system state interpretation and system initialization – long considered to be major theoretical pitfalls – have been solved easily. Although originally introduced for numerical simulation and identification of FDEs, this approach also provides original solutions to many problems such as the initial conditions of fractional derivatives, the uniqueness of FDS transients, formulation of analytical transients, fractional differentiation of functions, state observation and control, definition of fractional energy, and Lyapunov stability analysis of linear and nonlinear fractional order systems. This second volume focuses on the initialization, observation and control of the distributed state, followed by stability analysis of fractional differential systems.

Author : Feliz Manuel Minhós,João Fialho
Publisher : MDPI
Page : 158 pages
File Size : 45,9 Mb
Release : 2021-04-15
Category : Mathematics
ISBN : 9783036507101

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Nonlinear Differential Equations and Dynamical Systems by Feliz Manuel Minhós,João Fialho Pdf

This Special Edition contains new results on Differential and Integral Equations and Systems, covering higher-order Initial and Boundary Value Problems, fractional differential and integral equations and applications, non-local optimal control, inverse, and higher-order nonlinear boundary value problems, distributional solutions in the form of a finite series of the Dirac delta function and its derivatives, asymptotic properties’ oscillatory theory for neutral nonlinear differential equations, the existence of extremal solutions via monotone iterative techniques, predator–prey interaction via fractional-order models, among others. Our main goal is not only to show new trends in this field but also to showcase and provide new methods and techniques that can lead to future research.

Author : Aleksei Tepljakov
Publisher : Springer
Page : 184 pages
File Size : 45,8 Mb
Release : 2017-02-08
Category : Technology & Engineering
ISBN : 9783319529509

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Fractional-order Modeling and Control of Dynamic Systems by Aleksei Tepljakov Pdf

This book reports on an outstanding research devoted to modeling and control of dynamic systems using fractional-order calculus. It describes the development of model-based control design methods for systems described by fractional dynamic models. More than 300 years had passed since Newton and Leibniz developed a set of mathematical tools we now know as calculus. Ever since then the idea of non-integer derivatives and integrals, universally referred to as fractional calculus, has been of interest to many researchers. However, due to various issues, the usage of fractional-order models in real-life applications was limited. Advances in modern computer science made it possible to apply efficient numerical methods to the computation of fractional derivatives and integrals. This book describes novel methods developed by the author for fractional modeling and control, together with their successful application in real-world process control scenarios.