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Fractional Order Systems

Fractional Order Systems Book
Author : Ivo Petráš
Publisher : MDPI
Release : 2019-10-29
ISBN : 3039216082
Language : En, Es, Fr & De

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Book Description :

This book is focused on fractional order systems. Historically, fractional calculus has been recognized since the inception of regular calculus, with the first written reference dated in September 1695 in a letter from Leibniz to L’Hospital. Nowadays, fractional calculus has a wide area of applications in areas such as physics, chemistry, bioengineering, chaos theory, control systems engineering, and many others. In all those applications, we deal with fractional order systems in general. Moreover, fractional calculus plays an important role even in complex systems and therefore allows us to develop better descriptions of real-world phenomena. On that basis, fractional order systems are ubiquitous, as the whole real world around us is fractional. Due to this reason, it is urgent to consider almost all systems as fractional order systems. This Special Issue explores applications of such systems to control, synchronization, and various mathematical models, as for instance, MRI, long memory process, diffusion.

Fractional Order Systems

Fractional Order Systems Book
Author : Riccardo Caponetto
Publisher : World Scientific
Release : 2010
ISBN : 9814304204
Language : En, Es, Fr & De

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Book Description :

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.

Fractional order Systems and Controls

Fractional order Systems and Controls Book
Author : Concepción A. Monje,YangQuan Chen,Blas M. Vinagre,Dingyu Xue,Vicente Feliu-Batlle
Publisher : Springer Science & Business Media
Release : 2010-09-28
ISBN : 9781849963350
Language : En, Es, Fr & De

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Book Description :

Fractional-order Systems and Controls details the use of fractional calculus in the description and modeling of systems, and in a range of control design and practical applications. It is largely self-contained, covering the fundamentals of fractional calculus together with some analytical and numerical techniques and providing MATLAB® codes for the simulation of fractional-order control (FOC) systems. Many different FOC schemes are presented for control and dynamic systems problems. Practical material relating to a wide variety of applications is also provided. All the control schemes and applications are presented in the monograph with either system simulation results or real experimental results, or both. Fractional-order Systems and Controls provides readers with a basic understanding of FOC concepts and methods, so they can extend their use of FOC in other industrial system applications, thereby expanding their range of disciplines by exploiting this versatile new set of control techniques.

Mathematical Techniques of Fractional Order Systems

Mathematical Techniques of Fractional Order Systems Book
Author : Ahmad Taher Azar,Ahmed G. Radwan,Sundarapandian Vaidyanathan
Publisher : Elsevier
Release : 2018-06-11
ISBN : 012813593X
Language : En, Es, Fr & De

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Book Description :

Mathematical Techniques of Fractional Order Systems illustrates advances in linear and nonlinear fractional-order systems relating to many interdisciplinary applications, including biomedical, control, circuits, electromagnetics and security. The book covers the mathematical background and literature survey of fractional-order calculus and generalized fractional-order circuit theorems from different perspectives in design, analysis and realizations, nonlinear fractional-order circuits and systems, the fractional-order memristive circuits and systems in design, analysis, emulators, simulation and experimental results. It is primarily meant for researchers from academia and industry, and for those working in areas such as control engineering, electrical engineering, computer science and information technology. This book is ideal for researchers working in the area of both continuous-time and discrete-time dynamics and chaotic systems. Discusses multidisciplinary applications with new fundamentals, modeling, analysis, design, realization and experimental results Includes circuits and systems based on 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 applications in the book

Fractional Order Control Systems

Fractional Order Control Systems Book
Author : Dingyü Xue
Publisher : Walter de Gruyter GmbH & Co KG
Release : 2017-07-10
ISBN : 3110497190
Language : En, Es, Fr & De

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Book Description :

This book explains the essentials of fractional calculus and demonstrates its application in control system modeling, analysis and design. It presents original research to find high-precision solutions to fractional-order differentiations and differential equations. Numerical algorithms and their implementations are proposed to analyze multivariable fractional-order control systems. Through high-quality MATLAB programs, it provides engineers and applied mathematicians with theoretical and numerical tools to design control systems. Contents Introduction to fractional calculus and fractional-order control Mathematical prerequisites Definitions and computation algorithms of fractional-order derivatives and Integrals Solutions of linear fractional-order differential equations Approximation of fractional-order operators Modelling and analysis of multivariable fractional-order transfer function Matrices State space modelling and analysis of linear fractional-order Systems Numerical solutions of nonlinear fractional-order differential Equations Design of fractional-order PID controllers Frequency domain controller design for multivariable fractional-order Systems Inverse Laplace transforms involving fractional and irrational Operations FOTF Toolbox functions and models Benchmark problems for the assessment of fractional-order differential equation algorithms

Fractional Order Systems

Fractional Order Systems Book
Author : Ahmad Taher Azar,Ahmed G. Radwan,Sundarapandian Vaidyanathan
Publisher : Academic Press
Release : 2018-08-16
ISBN : 0128163089
Language : En, Es, Fr & De

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Book Description :

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

Advanced Synchronization Control and Bifurcation of Chaotic Fractional Order Systems

Advanced Synchronization Control and Bifurcation of Chaotic Fractional Order Systems Book
Author : Boulkroune, Abdesselem,Ladaci, Samir
Publisher : IGI Global
Release : 2018-05-11
ISBN : 152255419X
Language : En, Es, Fr & De

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Book Description :

In the recent years, fractional-order systems have been studied by many researchers in the engineering field. It was found that many systems can be described more accurately by fractional differential equations than by integer-order models. Advanced Synchronization Control and Bifurcation of Chaotic Fractional-Order Systems is a scholarly publication that explores new developments related to novel chaotic fractional-order systems, control schemes, and their applications. Featuring coverage on a wide range of topics including chaos synchronization, nonlinear control, and cryptography, this publication is geared toward engineers, IT professionals, researchers, and upper-level graduate students seeking current research on chaotic fractional-order systems and their applications in engineering and computer science.

Fractional Order Signal Processing

Fractional Order Signal Processing Book
Author : Saptarshi Das,Indranil Pan
Publisher : Springer Science & Business Media
Release : 2011-09-15
ISBN : 9783642231179
Language : En, Es, Fr & De

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Book Description :

The book tries to briefly introduce the diverse literatures in the field of fractional order signal processing which is becoming an emerging topic among an interdisciplinary community of researchers. This book is aimed at postgraduate and beginning level research scholars who would like to work in the field of Fractional Order Signal processing (FOSP). The readers should have preliminary knowledge about basic signal processing techniques. Prerequisite knowledge of fractional calculus is not essential and is exposited at relevant places in connection to the appropriate signal processing topics. Basic signal processing techniques like filtering, estimation, system identification, etc. in the light of fractional order calculus are presented along with relevant application areas. The readers can easily extend these concepts to varied disciplines like image or speech processing, pattern recognition, time series forecasting, financial data analysis and modeling, traffic modeling in communication channels, optics, biomedical signal processing, electrochemical applications and many more. Adequate references are provided in each category so that the researchers can delve deeper into each area and broaden their horizon of understanding. Available MATLAB tools to simulate FOSP theories are also introduced so that the readers can apply the theoretical concepts right-away and gain practical insight in the specific domain.

Fractional Order Systems Control Theory and Applications

Fractional Order Systems   Control Theory and Applications Book
Author : Omar Naifar,Abdellatif Ben Makhlouf
Publisher : Springer
Release : 2021-08-11
ISBN : 9783030714451
Language : En, Es, Fr & De

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Book Description :

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.

Stabilization and Control of Fractional Order Systems A Sliding Mode Approach

Stabilization and Control of Fractional Order Systems  A Sliding Mode Approach Book
Author : Bijnan Bandyopadhyay,Shyam Kamal
Publisher : Springer
Release : 2014-07-22
ISBN : 3319086219
Language : En, Es, Fr & De

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Book Description :

In the last two decades fractional differential equations have been used more frequently in physics, signal processing, fluid mechanics, viscoelasticity, mathematical biology, electro chemistry and many others. It opens a new and more realistic way to capture memory dependent phenomena and irregularities inside the systems by using more sophisticated mathematical analysis. This monograph is based on the authors’ work on stabilization and control design for continuous and discrete fractional order systems. The initial two chapters and some parts of the third chapter are written in tutorial fashion, presenting all the basic concepts of fractional order system and a brief overview of sliding mode control of fractional order systems. The other parts contain deal with robust finite time stability of fractional order systems, integral sliding mode control of fractional order systems, co-operative control of multi-agent systems modeled as fractional differential equation, robust stabilization of discrete fractional order systems, high performance control using soft variable structure control and contraction analysis by integer and fractional order infinitesimal variations.

Intelligent Fractional Order Systems and Control

Intelligent Fractional Order Systems and Control Book
Author : Indranil Pan,Saptarshi Das
Publisher : Springer
Release : 2012-08-23
ISBN : 3642315496
Language : En, Es, Fr & De

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Book Description :

Fractional order calculus is finding increasing interest in the control system community. Hardware realizations of fractional order controllers have sparked off a renewed zeal into the investigations of control system design in the light of fractional calculus. As such many notions of integer order LTI systems are being modified and extended to incorporate these new concepts. Computational Intelligence (CI) techniques have been applied to engineering problems to find solutions to many hitherto intractable conundrums and is a useful tool for dealing with problems of higher computational complexity. This book borders on the interface between CI techniques and fractional calculus, and looks at ways in which fractional order control systems may be designed or enhanced using CI based paradigms. To the best of the author’s knowledge this is the first book of its kind exclusively dedicated to the application of computational intelligence techniques in fractional order systems and control. The book tries to assimilate various existing concepts in this nascent field of fractional order intelligent control and is aimed at researchers and post graduate students working in this field.

Fractional Order Nonlinear Systems

Fractional Order Nonlinear Systems Book
Author : Ivo Petráš
Publisher : Springer Science & Business Media
Release : 2011-05-30
ISBN : 3642181015
Language : En, Es, Fr & De

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Book Description :

"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.

Advances in Synchronization of Coupled Fractional Order Systems

Advances in Synchronization of Coupled Fractional Order Systems Book
Author : Rafael Martínez-Guerra,Claudia Alejandra Pérez-Pinacho
Publisher : Springer
Release : 2018-07-23
ISBN : 3319939467
Language : En, Es, Fr & De

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Book Description :

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.

Robust Adaptive Control for Fractional Order Systems with Disturbance and Saturation

Robust Adaptive Control for Fractional Order Systems with Disturbance and Saturation Book
Author : Mou Chen,Shuyi Shao,Peng Shi
Publisher : John Wiley & Sons
Release : 2017-12-26
ISBN : 1119393272
Language : En, Es, Fr & De

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Book Description :

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.

Fractional Order Systems and Applications in Engineering

Fractional Order Systems and Applications in Engineering Book
Author : Dumitru Baleanu,Valentina Emilia Balas,Agarwal Praveen
Publisher : Academic Press
Release : 2021-08-15
ISBN : 9780323909532
Language : En, Es, Fr & De

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Book Description :

Fractional Order Systems and Applications in Engineering presents the use of fractional calculus (calculus of non-integer order) in the description and modelling of systems and in a range of control design and practical applications. The book covers the fundamentals of fractional calculus together with some analytical and numerical techniques, and provides MATLAB® codes for the simulation of fractional-order control (FOC) systems. The use of fractional calculus can improve and generalize well-established control methods and strategies. Many different FOC schemes are presented for control and dynamic systems problems. These extend to the challenging control engineering design problems of robust and nonlinear control. Practical material relating to a wide variety of applications including, among others, mechatronics, civil engineering, irrigation and water management, and biological systems is also provided. All the control schemes and applications are presented with either system simulation results or real experimental results, or both. Fractional Order Systems and Applications in Engineering introduces readers to the essentials of FOC and imbues them with a basic understanding of FOC concepts and methods. With this knowledge readers can extend their use of FOC in other industrial system applications, thereby expanding their range of disciplines by exploiting this versatile new set of control techniques. Provides the most recent and up-to-date developments on the Fractional-order Systems and their analyzing process Integrates recent advancements of modeling of real phenomena (on Fractional-order Systems) via different-different mathematical equations with demonstrated applications in numerous seemingly diverse and widespread fields of science and engineering Provides readers with illustrative examples of how to use the presented theories of Fractional-order Systems in specific cases with associated MATLAB code

Bifurcation and Chaos in Fractional Order Systems

Bifurcation and Chaos in Fractional Order Systems Book
Author : Marius-F. Danca,Guanrong Chen
Publisher : MDPI
Release : 2021-01-19
ISBN : 3036500928
Language : En, Es, Fr & De

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Book Description :

This book presents a collection of seven technical papers on fractional-order complex systems, especially chaotic systems with hidden attractors and symmetries, in the research front of the field, which will be beneficial for scientific researchers, graduate students, and technical professionals to study and apply. It is also suitable for teaching lectures and for seminars to use as a reference on related topics.

Artificial Neural Networks Methods and Applications in Fractional Order Systems

Artificial Neural Networks  Methods and Applications in Fractional Order Systems Book
Author : Snehashish Chakraverty,Susmita Mall
Publisher : Unknown
Release : 2021-01-14
ISBN : 9789811218804
Language : En, Es, Fr & De

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Book Description :

This is the first book that uses Artificial Neural Networks (ANN) to solve fractional order systems. As a powerful data modeling tool, information is processed through neurons in parallel manner to solve a specific problem. Knowledge is acquired through learning and stored with inter neuron connections strength which are expressed by numerical values called weights. These weights are used to complete output signal values for new testing input signal value.In this book, multi-layer ANN model will be used to handle fractional order differential equations (FDEs). The network is trained using a back-propagation unsupervised learning algorithm which is based on the gradient descent rule. The ANN approximate solution of FDEs may be expressed as a sum of two terms; the first part satisfies boundary or initial conditions, and the second term contains ANN output with network parameters (weights and biases).Next, single layer Functional Link Artificial Neural Network (FLANN) models will be included for solving the FDEs. In FLANN the hidden layer is replaced by a functional expansion block for enhancement of the input patterns using orthogonal polynomials such as Chebyshev, Legendre, Hermite, etc. The computations become efficient because the procedure does not need to have hidden layer. Thus, the numbers of network parameters are less than the traditional ANN model.Varieties of FDEs will be addressed to show the reliability and efffectiveness of ANN. Singular nonlinear fractional Lane-Emden type equations, fractional vibration problems viz. Bagley-Torvik equations, fractional electrical problems viz. RLC, RC, LC circuit problems, Duffing oscillator problems with fractional derivatives etc. will be handled using multi-layer ANN and single layer FLANN models.

Fractional order Systems Without Equilibria The First Example of Hyperchaos and Its Application to Synchronization

Fractional order Systems Without Equilibria  The First Example of Hyperchaos and Its Application to Synchronization Book
Author : Anonim
Publisher : Unknown
Release : 2015
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Abstract A challenging topic in nonlinear dynamics concerns the study of fractional-order systems without equilibrium points. In particular, no paper has been published to date regarding the presence of hyperchaos in these systems. This paper aims to bridge the gap by introducing a new example of fractional-order hyperchaotic system without equilibrium points. The conducted analysis shows that hyperchaos exists in the proposed system when its order is as low as 3.84. Moreover, an interesting application of hyperchaotic synchronization to the considered fractional-order system is provided.

Fractional order Modeling and Control of Dynamic Systems

Fractional order Modeling and Control of Dynamic Systems Book
Author : Aleksei Tepljakov
Publisher : Springer
Release : 2017-02-08
ISBN : 3319529501
Language : En, Es, Fr & De

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Book Description :

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.

Analysis Modeling and Stability of Fractional Order Differential Systems 1

Analysis  Modeling and Stability of Fractional Order Differential Systems 1 Book
Author : Jean-Claude Trigeassou,Nezha Maamri
Publisher : John Wiley & Sons
Release : 2019-08-06
ISBN : 111964884X
Language : En, Es, Fr & De

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Book Description :

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.