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| functional fractional calculus for system identification and controls: Functional Fractional Calculus for System Identification and Controls Shantanu Das, 2007-09-26 In this book, not only are mathematical abstractions discussed in a lucid manner, but also several practical applications are given particularly for system identification, description and then efficient controls. The reader gets a feeling of the wide applicability of fractional calculus in the field of science and engineering. With this book, a starter can understand the concepts of this emerging field with a minimal effort and basic mathematics. |
| functional fractional calculus for system identification and controls: Functional Fractional Calculus Shantanu Das, 2011-06-01 When a new extraordinary and outstanding theory is stated, it has to face criticism and skeptism, because it is beyond the usual concept. The fractional calculus though not new, was not discussed or developed for a long time, particularly for lack of its application to real life problems. It is extraordinary because it does not deal with ‘ordinary’ differential calculus. It is outstanding because it can now be applied to situations where existing theories fail to give satisfactory results. In this book not only mathematical abstractions are discussed in a lucid manner, with physical mathematical and geometrical explanations, but also several practical applications are given particularly for system identification, description and then efficient controls. The normal physical laws like, transport theory, electrodynamics, equation of motions, elasticity, viscosity, and several others of are based on ‘ordinary’ calculus. In this book these physical laws are generalized in fractional calculus contexts; taking, heterogeneity effect in transport background, the space having traps or islands, irregular distribution of charges, non-ideal spring with mass connected to a pointless-mass ball, material behaving with viscous as well as elastic properties, system relaxation with and without memory, physics of random delay in computer network; and several others; mapping the reality of nature closely. The concept of fractional and complex order differentiation and integration are elaborated mathematically, physically and geometrically with examples. The practical utility of local fractional differentiation for enhancing the character of singularity at phase transition or characterizing the irregularity measure of response function is deliberated. Practical results of viscoelastic experiments, fractional order controls experiments, design of fractional controller and practical circuit synthesis for fractional order elements are elaborated in this book. The book also maps theory of classical integer order differential equations to fractional calculus contexts, and deals in details with conflicting and demanding initialization issues, required in classical techniques. The book presents a modern approach to solve the ‘solvable’ system of fractional and other differential equations, linear, non-linear; without perturbation or transformations, but by applying physical principle of action-and-opposite-reaction, giving ‘approximately exact’ series solutions. Historically, Sir Isaac Newton and Gottfried Wihelm Leibniz independently discovered calculus in the middle of the 17th century. In recognition to this remarkable discovery, J.von Neumann remarked, “...the calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more equivocally than anything else the inception of modern mathematical analysis which is logical development, still constitute the greatest technical advance in exact thinking.” This XXI century has thus started to ‘think-exactly’ for advancement in science & technology by growing application of fractional calculus, and this century has started speaking the language which nature understands the best. |
| functional fractional calculus for system identification and controls: Fractional-order Modeling and Control of Dynamic Systems Aleksei Tepljakov, 2017-02-08 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. |
| functional fractional calculus for system identification and controls: Fractional Dynamical Systems: Methods, Algorithms and Applications Piotr Kulczycki, Józef Korbicz, Janusz Kacprzyk, 2022-01-04 This book presents a wide and comprehensive spectrum of issues and problems related to fractional-order dynamical systems. It is meant to be a full-fledge, comprehensive presentation of many aspects related to the broadly perceived fractional-order dynamical systems which constitute an extension of the traditional integer-order-type descriptions. This implies far-reaching consequences, both analytic and algorithmic, because—in general—properties of the traditional integer-order systems cannot be directly extended by a straightforward generalization to fractional-order systems, modeled by fractional-order differential equations involving derivatives of an non-integer order. This can be useful for describing and analyzing, for instance, anomalies in the behavior of various systems, chaotic behavior, etc. The book contains both analytic contributions with state-of-the-art and theoretical foundations, algorithmic implementation of tools and techniques, and—finally—some examples of relevant and successful practical applications. |
| functional fractional calculus for system identification and controls: Sliding Modes after the first Decade of the 21st Century Leonid Fridman, Jaime Moreno, Rafael Iriarte, 2011-09-10 The book presents the newest results of the major world research groups working in the area of Variable Structure Systems and Sliding Mode Control (VSS/SMC). The research activity of these groups is coordinated by the IEEE Technical Committee on Variable Structure Systems (VSS) and Sliding Modes (SM). The presented results include the reports of the research groups collaborating in a framework of the Unión European Union – México project of Fondo de Cooperación Internacional en Ciencia y Tecnología (FONCICyT) 93302 titled Automatization and Monitoring of Energy Production Processes via Sliding Mode Control. The book starts with the overview of the sliding mode control concepts and algorithms that were developed and discussed in the last two decades The research papers are combined in three sections: Part I: VSS and SM Algorithms and their Analysis Part II: SMC Design Part III: Applications of VSS and SMC The book will be of interests of engineers, researchers and graduate students working in the area of the control systems design. Novel mathematical theories and engineering concepts of control systems are rigorously discussed and supported by numerous applications to practical tasks. |
| functional fractional calculus for system identification and controls: Recent Advances in Intelligent Information Systems and Applied Mathematics Oscar Castillo, Dipak Kumar Jana, Debasis Giri, Arif Ahmed, 2020-01-31 This book describes the latest advances in intelligent techniques such as fuzzy logic, neural networks, and optimization algorithms, and their relevance in building intelligent information systems in combination with applied mathematics. The authors also outline the applications of these systems in areas like intelligent control and robotics, pattern recognition, medical diagnosis, time series prediction, and optimization of complex problems. By sharing fresh ideas and identifying new targets/problems it offers young researchers and students new directions for their future research. The book is intended for readers from mathematics and computer science, in particular professors and students working on theory and applications of intelligent systems for real-world applications. |
| functional fractional calculus for system identification and controls: Fractional Order Signal Processing Saptarshi Das, Indranil Pan, 2011-09-15 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. |
| functional fractional calculus for system identification and controls: Progress in Systems Engineering Henry Selvaraj, Dawid Zydek, Grzegorz Chmaj, 2014-08-12 This collection of proceedings from the International Conference on Systems Engineering, Las Vegas, 2014 is orientated toward systems engineering, including topics like aero-space, power systems, industrial automation and robotics, systems theory, control theory, artificial intelligence, signal processing, decision support, pattern recognition and machine learning, information and communication technologies, image processing, and computer vision as well as its applications. The volume’s main focus is on models, algorithms, and software tools that facilitate efficient and convenient utilization of modern achievements in systems engineering. |
| functional fractional calculus for system identification and controls: Advances in the Theory and Applications of Non-integer Order Systems Wojciech Mitkowski, Janusz Kacprzyk, Jerzy Baranowski, 2013-06-03 This volume presents various aspects of non-integer order systems, also known as fractional systems, which have recently attracted an increasing attention in the scientific community of systems science, applied mathematics, control theory. Non-integer systems have become relevant for many fields of science and technology exemplified by the modeling of signal transmission, electric noise, dielectric polarization, heat transfer, electrochemical reactions, thermal processes, acoustics, etc. The content is divided into six parts, every of which considers one of the currently relevant problems. In the first part the Realization problem is discussed, with a special focus on positive systems. The second part considers stability of certain classes of non-integer order systems with and without delays. The third part is focused on such important aspects as controllability, observability and optimization especially in discrete time. The fourth part is focused on distributed systems where non-integer calculus leads to new and interesting results. The next part considers problems of solutions and approximations of non-integer order equations and systems. The final and most extensive part is devoted to applications. Problems from mechatronics, biomedical engineering, robotics and others are all analyzed and solved with tools from fractional systems. This volume came to fruition thanks to high level of talks and interesting discussions at RRNR 2013 - 5th Conference on Non-integer Order Calculus and its Applications that took place at AGH University of Science and Technology in Kraków, Poland, which was organized by the Faculty of Electrical Engineering, Automatics, Computer Science and Biomedical Engineering. |
| functional fractional calculus for system identification and controls: Boundary Value Problems For Fractional Differential Equations And Systems Bashir Ahmad, Johnny L Henderson, Rodica Luca, 2021-02-18 This book is devoted to the study of existence of solutions or positive solutions for various classes of Riemann-Liouville and Caputo fractional differential equations, and systems of fractional differential equations subject to nonlocal boundary conditions. The monograph draws together many of the authors' results, that have been obtained and highly cited in the literature in the last four years.In each chapter, various examples are presented which support the main results. The methods used in the proof of these theorems include results from the fixed point theory and fixed point index theory. This volume can serve as a good resource for mathematical and scientific researchers, and for graduate students in mathematics and science interested in the existence of solutions for fractional differential equations and systems. |
| functional fractional calculus for system identification and controls: Discrete Fractional Calculus Piotr Ostalczyk, 2015-11-26 The main subject of the monograph is the fractional calculus in the discrete version. The volume is divided into three main parts. Part one contains a theoretical introduction to the classical and fractional-order discrete calculus where the fundamental role is played by the backward difference and sum. In the second part, selected applications of the discrete fractional calculus in the discrete system control theory are presented. In the discrete system identification, analysis and synthesis, one can consider integer or fractional models based on the fractional-order difference equations. The third part of the book is devoted to digital image processing. |
| functional fractional calculus for system identification and controls: Positive Systems Filippo Cacace, Lorenzo Farina, Roberto Setola, Alfredo Germani, 2017-04-01 This book presents high-quality original contributions on positive systems, including topics such as: monotone dynamical systems in mathematical biology and game theory; mathematical developments for networked systems in biology, chemistry and the social sciences; linear and nonlinear positive operators; dynamical analysis, observation and control of positive distributed parameter systems; stochastic realization theory; biological systems with positive variables and positive controls; iterated function systems; nonnegative dynamic processes; and dimensioning problems for collaborative systems. The book comprises a selection of the best papers presented at the POSTA 2016, the 5th International Symposium on Positive Systems, which was held in Rome, Italy, in September 2016. This conference series represents a targeted response to the growing need for research that reports on and critically discusses a wide range of topics concerning the theory and applications of positive systems. |
| functional fractional calculus for system identification and controls: Fractional Dynamics and Control Dumitru Baleanu, José António Tenreiro Machado, Albert C. J. Luo, 2011-11-19 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. |
| functional fractional calculus for system identification and controls: Fractional Order Systems—Control Theory and Applications Omar Naifar, Abdellatif Ben Makhlouf, 2021-08-30 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. |
| functional fractional calculus for system identification and controls: Proceedings of the 4th International Conference on Communication, Devices and Computing Dilip Kumar Sarkar, Pradip Kumar Sadhu, Sunandan Bhunia, Jagannath Samanta, Suman Paul, 2023-07-27 The book is a collection of best selected research papers presented at the Fourth International Conference on Communication, Devices and Computing (ICCDC 2023). The book covers new ideas, applications and experiences of research engineers, scientists, industrialists, scholars and students from in and around the globe. It covers research contributions from communication technologies which are from the areas such as 5G communication, next-generation Wi-Fi, spread spectrum systems, satellite and high altitude platforms, radio over fiber techniques, wireless sensor networks, modulation and diversity technique, ad hoc and mesh networks, cognitive radio networking, optical wireless and visible light communications, signal processing for secure communication, millimeter wave and terahertz communication, design, control and management of optical network, error control coding and information theory, printed antennas, performance analysis of wireless network, smart antennas and space time processing. |
| functional fractional calculus for system identification and controls: Fractional Order Systems Riccardo Caponetto, 2010 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. |
| functional fractional calculus for system identification and controls: Cybernetics, Cognition and Machine Learning Applications Vinit Kumar Gunjan, P. N. Suganthan, Jan Haase, Amit Kumar, Balasubramanian Raman, 2020-04-20 This book provides a collection of selected papers presented at the International Conference on Cybernetics, Cognition and Machine Learning Applications (ICCCMLA 2019), which was held in Goa, India, on 16–17 August 2019. It covers the latest research trends and advances in the areas of data science, artificial intelligence, neural networks, cognitive science and machine learning applications, cyber-physical systems, and cybernetics. |
| functional fractional calculus for system identification and controls: Automatic Control, Robotics, and Information Processing Piotr Kulczycki, Józef Korbicz, Janusz Kacprzyk, 2020-09-03 This book presents a wide and comprehensive range of issues and problems in various fields of science and engineering, from both theoretical and applied perspectives. The desire to develop more effective and efficient tools and techniques for dealing with complex processes and systems has been a natural inspiration for the emergence of numerous fields of science and technology, in particular control and automation and, more recently, robotics. The contributions gathered here concern the development of methods and algorithms to determine best practices regarding broadly perceived decisions or controls. From an engineering standpoint, many of them focus on how to automate a specific process or complex system. From a tools-based perspective, several contributions address the development of analytic and algorithmic methods and techniques, devices and systems that make it possible to develop and subsequently implement the automation and robotization of crucial areas of human activity. All topics discussed are illustrated with sample applications. |
| functional fractional calculus for system identification and controls: Automation 2017 Roman Szewczyk, Cezary Zieliński, Małgorzata Kaliczyńska, 2017-02-28 This book consists of papers presented at Automation 2017, an international conference held in Warsaw from March 15 to 17, 2017. It discusses research findings associated with the concepts behind INDUSTRY 4.0, with a focus on offering a better understanding of and promoting participation in the Fourth Industrial Revolution. Each chapter presents a detailed analysis of a specific technical problem, in most cases followed by a numerical analysis, simulation and description of the results of implementing the solution in a real-world context. The theoretical results, practical solutions and guidelines presented are valuable for both researchers working in the area of engineering sciences and practitioners looking for solutions to industrial problems. |
| functional fractional calculus for system identification and controls: Automation 2019 Roman Szewczyk, Cezary Zieliński, Małgorzata Kaliczyńska, 2019-02-15 This book consists of papers presented at AUTOMATION2019, an international conference held in Warsaw from March 27 to 29, 2019. It discusses the radical technological changes occurring due to the INDUSTRY 4.0. To follow these changes, both scientists and engineers have to face the challenge of interdisciplinary approach directed at the development of cyber-physical systems. This approach encompasses interdisciplinary theoretical knowledge, numerical modelling and simulation as well as application of artificial intelligence techniques. Both software and physical devices are composed into systems that will increase production efficiency and resource savings. The theoretical results, practical solutions and guidelines presented are valuable for both researchers working in the area of engineering sciences and practitioners looking for solutions to industrial problems. |
| functional fractional calculus for system identification and controls: Entropy in Dynamic Systems Jan Awrejcewicz, J. A. Tenreiro Machado, 2019-10-16 In order to measure and quantify the complex behavior of real-world systems, either novel mathematical approaches or modifications of classical ones are required to precisely predict, monitor, and control complicated chaotic and stochastic processes. Though the term of entropy comes from Greek and emphasizes its analogy to energy, today, it has wandered to different branches of pure and applied sciences and is understood in a rather rough way, with emphasis placed on the transition from regular to chaotic states, stochastic and deterministic disorder, and uniform and non-uniform distribution or decay of diversity. This collection of papers addresses the notion of entropy in a very broad sense. The presented manuscripts follow from different branches of mathematical/physical sciences, natural/social sciences, and engineering-oriented sciences with emphasis placed on the complexity of dynamical systems. Topics like timing chaos and spatiotemporal chaos, bifurcation, synchronization and anti-synchronization, stability, lumped mass and continuous mechanical systems modeling, novel nonlinear phenomena, and resonances are discussed. |
| functional fractional calculus for system identification and controls: Outliers in Control Engineering Paweł D. Domański, YangQuan Chen, Maciej Ławryńczuk, 2022-03-07 Outliers play an important, though underestimated, role in control engineering. Traditionally they are unseen and neglected. In opposition, industrial practice gives frequent examples of their existence and their mostly negative impacts on the control quality. The origin of outliers is never fully known. Some of them are generated externally to the process (exogenous), like for instance erroneous observations, data corrupted by control systems or the effect of human intervention. Such outliers appear occasionally with some unknow probability shifting real value often to some strange and nonsense value. They are frequently called deviants, anomalies or contaminants. In most cases we are interested in their detection and removal. However, there exists the second kind of outliers. Quite often strange looking data observations are not artificial data occurrences. They may be just representatives of the underlying generation mechanism being inseparable internal part of the process (endogenous outliers). In such a case they are not wrong and should be treated with cautiousness, as they may include important information about the dynamic nature of the process. As such they cannot be neglected nor simply removed. The Outlier should be detected, labelled and suitably treated. These activities cannot be performed without proper analytical tools and modeling approaches. There are dozens of methods proposed by scientists, starting from Gaussian-based statistical scoring up to data mining artificial intelligence tools. The research presented in this book presents novel approach incorporating non-Gaussian statistical tools and fractional calculus approach revealing new data analytics applied to this important and challenging task. The proposed book includes a collection of contributions addressing different yet cohesive subjects, like dynamic modelling, classical control, advanced control, fractional calculus, statistical analytics focused on an ultimate goal: robust and outlier-proof analysis. All studied problems show that outliers play an important role and classical methods, in which outlier are not taken into account, do not give good results. Applications from different engineering areas are considered such as semiconductor process control and monitoring, MIMO peltier temperature control and health monitoring, networked control systems, and etc. |
| functional fractional calculus for system identification and controls: Modeling, Optimization and Intelligent Control Techniques in Renewable Energy Systems Moussa Labbadi, Kamal Elyaalaoui, Loubna Bousselamti, Mohammed Ouassaid, Mohamed Cherkaoui, 2022-04-14 This book consists of two parts. The first part studies selected recent developed strategies of control and management for renewable energy resources. The strategies of control are tested in the presence of unbalance power, voltage faults, frequency deviation, wind speed variation and parametric uncertainties. The second part is especially focused on study of hybrid photovoltaic (PV)-Concentrated solar power (CSP) coupled to a thermal storage system. It gathers a set of chapters covering recent survey literature, modelling and optimization of hybrid PV-CSP power plants. In this part, a detailed model of hybrid PV-CSP with thermal storage system is presented and smart optimization techniques like particle swarm optimization (PSO) and genetic algorithm (GA) are also described and used to optimally design the hybrid PV-CSP renewable energy system. The book would be interesting to most academic undergraduate, postgraduates, researchers on renewable energy systems in terms of modeling, optimization and control, as well as the satisfaction of grid code requirements. Also, it provides an excellent background to renewable energy sources, it is an excellent choice for energy engineers, researchers, system operators, and graduate students. This book can used as a good reference for the academic research on the smart grid, power control, integration of renewable energy sources, and related to this or used in Ph.D study of control, optimisation, management problems and their application in field engineering. |
| functional fractional calculus for system identification and controls: Proceedings of the International Conference on Fractional Differentiation and its Applications (ICFDA’21) Andrzej Dzielinski, Dominik Sierociuk, Piotr Ostalczyk, 2022-04-26 This book touches upon various aspects of a very interesting, and growing in popularity category of models of dynamical systems. These are the so-called fractional-order systems. Such models are not only relevant for many fields of science and technology, but may also find numerous applications in other disciplines applying the mathematical modelling tools. Thus, the book is intended for a very wide audience of professionals who want to expand their knowledge of systems modelling and its applications. The book includes the selections of papers presented at the International Conference on Fractional Calculus and its Applications organized by the Warsaw University of Technology and was held online on 6–8 September 2021. The International Conference on Fractional Calculus and its Applications (ICFDA) has an almost twenty years history. It started in Bordeaux (France) in 2004, followed by Porto (Portugal) 2006, Istanbul (Turkey) 2008, Badajoz (Spain) 2010, Nanjing (China) 2012, Catania (Italy) 2014, Novi Sad (Serbia) 2016, Amman (Jordan) 2018. Next ICFDA was planned in 2020 in Warsaw (Poland), but COVID-19 pandemic shifted it to 6–8 September 2021. Hence, the organizers were forced to change the form of the conference to the online one. In the volume twenty eight high-quality research papers presented during the ICFDA 2021 eleven Regular Sessions with an additional online Discussion Session are presented. The presented papers are scientifically inspiring, leading to new fruitful ideas. They cover a very broad range of many disciplines. Nowadays, and especially in such a subject as fractional calculus, it is very difficult to assign papers to specific scientific areas. So, many of the papers included have an interdisciplinary character. |
| functional fractional calculus for system identification and controls: CONTROLO 2024 Antonio Pedro Aguiar, Paula Rocha Malonek, Vítor Hugo Pinto, Fernando A. C. C. Fontes, Roman Chertovskih, 2025-04-22 This book offers a perfect insight of the latest research and developments in the fields of dynamic systems and control engineering. Gathering the proceedings of the 16th APCA International Conference on Automatic Control and Soft Computing (CONTROLO 2024), held on July 17-19, 2024, in Porto, Portugal, this volume covers a wide range of theoretical and practical issues relating to the development and use of different control approaches, such as PID control, adaptive control, non-linear control, intelligent monitoring and control based on fuzzy and neural systems. Further topics include robust control systems, and real time control. Sensors and actuators, measurement systems, renewable energy systems, aeronautic and aerospace systems, as well as industrial control and automation, are also comprehensively covered. All in all, this book offers a timely and thoroughly survey of the latest research in the fields of dynamic systems and automatic control engineering, and a source of inspiration for researchers and professionals worldwide. |
| functional fractional calculus for system identification and controls: Fractional-Order Modeling of Dynamic Systems with Applications in Optimization, Signal Processing, and Control Ahmed G. Radwan, Farooq Ahmad Khanday, Lobna A. Said, 2021-10-22 Fractional-order Modelling of Dynamic Systems with Applications in Optimization, Signal Processing and Control introduces applications from a design perspective, helping readers plan and design their own applications. The book includes the different techniques employed to design fractional-order systems/devices comprehensively and straightforwardly. Furthermore, mathematics is available in the literature on how to solve fractional-order calculus for system applications. This book introduces the mathematics that has been employed explicitly for fractional-order systems. It will prove an excellent material for students and scholars who want to quickly understand the field of fractional-order systems and contribute to its different domains and applications. Fractional-order systems are believed to play an essential role in our day-to-day activities. Therefore, several researchers around the globe endeavor to work in the different domains of fractional-order systems. The efforts include developing the mathematics to solve fractional-order calculus/systems and to achieve the feasible designs for various applications of fractional-order systems. - Presents a simple and comprehensive understanding of the field of fractional-order systems - Offers practical knowledge on the design of fractional-order systems for different applications - Exposes users to possible new applications for fractional-order systems |
| functional fractional calculus for system identification and controls: Fractional Order Systems Ahmed G. Radwan, Farooq Ahmad Khanday, Lobna A. Said, 2021-10-13 Fractional Order Systems: An Overview of Mathematics, Design, and Applications for Engineers introduces applications from a design perspective, helping readers plan and design their own applications. The book includes the different techniques employed to design fractional-order systems/devices comprehensively and straightforwardly. Furthermore, mathematics is available in the literature on how to solve fractional-order calculus for system applications. This book introduces the mathematics that has been employed explicitly for fractional-order systems. It will prove an excellent material for students and scholars who want to quickly understand the field of fractional-order systems and contribute to its different domains and applications. Fractional-order systems are believed to play an essential role in our day-to-day activities. Therefore, several researchers around the globe endeavor to work in the different domains of fractional-order systems. The efforts include developing the mathematics to solve fractional-order calculus/systems and to achieve the feasible designs for various applications of fractional-order systems. - Presents a simple and comprehensive understanding of the field of fractional-order systems - Offers practical knowledge on the design of fractional-order systems for different applications - Exposes users to possible new applications for fractional-order systems |
| functional fractional calculus for system identification and controls: Generalized Fractional Order Differential Equations Arising in Physical Models Santanu Saha Ray, Subhadarshan Sahoo, 2018-11-13 This book analyzes the various semi-analytical and analytical methods for finding approximate and exact solutions of fractional order partial differential equations. It explores approximate and exact solutions obtained by various analytical methods for fractional order partial differential equations arising in physical models. |
| functional fractional calculus for system identification and controls: Theoretical Developments and Applications of Non-Integer Order Systems Stefan Domek, Paweł Dworak, 2015-08-20 This volume is devoted to presentation of new results of research on systems of non-integer order, called also fractional systems. Their analysis and practical implementation have been the object of spontaneous development for a few last decades. The fractional order models can depict a physical plant better than the classical integer order ones. This covers different research fields such as insulator properties, visco-elastic materials, electrodynamic, electrothermal, electrochemical, economic processes modelling etc. On the other hand fractional controllers often outperform their integer order counterparts. This volume contains new ideas and examples of implementation, theoretical and pure practical aspects of using a non-integer order calculus. It is divided into four parts covering: mathematical fundamentals, modeling and approximations, controllability, observability and stability problems and practical applications of fractional control systems. The first part expands the base of tools and methods of the mathematical basis for non-integer order calculus. Part two focuses on new methods and developments in process modeling and fractional derivatives approximations. In the third part a bunch of papers which raise problems of controllability, observability and stability of non-integer order systems is provided. Part four is devoted to presentation of different fractional order control applications. This book was created thanks to many experts in the field of fractional calculus: authors, anonymous referees whose comments allowed us to improve the final form of the papers and active and inspiring discussion of the participants of RRNR'2015, the 7th Conference on Non-Integer Order Calculus and Its Applications that was organized by the Faculty of Electrical Engineering, West Pomeranian University of Technology, Szczecin, Poland. |
| functional fractional calculus for system identification and controls: Automation 2018 Roman Szewczyk, Cezary Zieliński, Małgorzata Kaliczyńska, 2018-03-07 This book consists of papers presented at Automation 2018, an international conference held in Warsaw from March 21 to 23, 2018. It discusses the radical technological changes occurring due to the INDUSTRY 4.0, with a focus on offering a better understanding of the Fourth Industrial Revolution. Each chapter presents a detailed analysis of interdisciplinary knowledge, numerical modeling and simulation as well as the application of cyber-physical systems, where information technology and physical devices create synergic systems leading to unprecedented efficiency. The theoretical results, practical solutions and guidelines presented are valuable for both researchers working in the area of engineering sciences and practitioners looking for solutions to industrial problems. |
| functional fractional calculus for system identification and controls: Basic Theory Anatoly Kochubei, Yuri Luchko, 2019-02-19 This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This first volume collects authoritative chapters covering the mathematical theory of fractional calculus, including fractional-order operators, integral transforms and equations, special functions, calculus of variations, and probabilistic and other aspects. |
| functional fractional calculus for system identification and controls: Advanced, Contemporary Control Andrzej Bartoszewicz, Jacek Kabziński, Janusz Kacprzyk, 2020-06-24 This book presents the proceedings of the 20th Polish Control Conference. A triennial event that was first held in 1958, the conference successfully combines its long tradition with a modern approach to shed light on problems in control engineering, automation, robotics and a wide range of applications in these disciplines. The book presents new theoretical results concerning the steering of dynamical systems, as well as industrial case studies and worked solutions to real-world problems in contemporary engineering. It particularly focuses on the modelling, identification, analysis and design of automation systems; however, it also addresses the evaluation of their performance, efficiency and reliability. Other topics include fault-tolerant control in robotics, automated manufacturing, mechatronics and industrial systems. Moreover, it discusses data processing and transfer issues, covering a variety of methodologies, including model predictive, robust and adaptive techniques, as well as algebraic and geometric methods, and fractional order calculus approaches. The book also examines essential application areas, such as transportation and autonomous intelligent vehicle systems, robotic arms, mobile manipulators, cyber-physical systems, electric drives and both surface and underwater marine vessels. Lastly, it explores biological and medical applications of the control-theory-inspired methods. |
| functional fractional calculus for system identification and controls: Simulation and Modeling Methodologies, Technologies and Applications Mohammad S. Obaidat, Tuncer Ören, Janusz Kacprzyk, Joaquim Filipe, 2016-01-14 The present book includes a set of selected extended papers from the 4th International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH 2014), held in Vienna, Austria, from 28 to 30 August 2014. The conference brought together researchers, engineers and practitioners interested in methodologies and applications of modeling and simulation. New and innovative solutions are reported in this book. SIMULTECH 2014 received 167 submissions, from 45 countries, in all continents. After a double blind paper review performed by the Program Committee, 23% were accepted as full papers and thus selected for oral presentation. Additional papers were accepted as short papers and posters. A further selection was made after the Conference, based also on the assessment of presentation quality and audience interest, so that this book includes the extended and revised versions of the very best papers of SIMULTECH 2014. Commitment to high quality standards is a major concern of SIMULTECH that will be maintained in the next editions, considering not only the stringent paper acceptance ratios but also the quality of the program committee, keynote lectures, participation level and logistics. |
| functional fractional calculus for system identification and controls: Power Electronics and Renewable Energy Systems C. Kamalakannan, L. Padma Suresh, Subhransu Sekhar Dash, Bijaya Ketan Panigrahi, 2014-11-19 The book is a collection of high-quality peer-reviewed research papers presented in the Proceedings of International Conference on Power Electronics and Renewable Energy Systems (ICPERES 2014) held at Rajalakshmi Engineering College, Chennai, India. These research papers provide the latest developments in the broad area of Power Electronics and Renewable Energy. The book discusses wide variety of industrial, engineering and scientific applications of the emerging techniques. It presents invited papers from the inventors/originators of new applications and advanced technologies. |
| functional fractional calculus for system identification and controls: Advanced Applications of Fractional Differential Operators to Science and Technology Matouk, Ahmed Ezzat, 2020-04-24 Fractional-order calculus dates to the 19th century but has been resurrected as a prevalent research subject due to its provision of more adequate and realistic descriptions of physical aspects within the science and engineering fields. What was once a classical form of mathematics is currently being reintroduced as a new modeling technique that engineers and scientists are finding modern uses for. There is a need for research on all facets of these fractional-order systems and studies of its potential applications. Advanced Applications of Fractional Differential Operators to Science and Technology provides emerging research exploring the theoretical and practical aspects of novel fractional modeling and related dynamical behaviors as well as its applications within the fields of physical sciences and engineering. Featuring coverage on a broad range of topics such as chaotic dynamics, ecological models, and bifurcation control, this book is ideally designed for engineering professionals, mathematicians, physicists, analysts, researchers, educators, and students seeking current research on fractional calculus and other applied mathematical modeling techniques. |
| functional fractional calculus for system identification and controls: The Craft of Fractional Modelling in Science and Engineering Jordan Hristov, 2018-06-22 This book is a printed edition of the Special Issue The Craft of Fractional Modelling in Science and Engineering that was published in Fractal Fract |
| functional fractional calculus for system identification and controls: Fractional Order Systems Ahmad Taher Azar, Ahmed G. Radwan, Sundarapandian Vaidyanathan, 2018-08-16 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 |
| functional fractional calculus for system identification and controls: Manufacturing Technologies and Production Systems Abhineet Saini, B. S. Pabla, Chander Prakash, Gurmohan Singh, Alokesh Pramanik, 2023-11-15 The book, which is part of a two-volume handbook set, presents a collection of recent advances in the field of industrial engineering, design, and related technologies. It includes state-of-the-art research conducted in the fields of Industry 4.0/5.0, smart systems/industries, robotics and automation, automobile engineering, thermal and fluid engineering, and its implementation. Manufacturing Technologies and Production Systems: Principles and Practices offers a comprehensive description of the developments in industrial engineering primarily focusing on industrial design, automotive engineering, construction and structural engineering, thermo-fluid mechanics, and interdisciplinary domains. The book captures emerging areas of materials science and advanced manufacturing engineering and presents the most recent trends in research for emerging researchers, field engineers, and academic professionals. |
| functional fractional calculus for system identification and controls: Fractional-Order Models for Nuclear Reactor Analysis Gilberto Espinosa Paredes, 2020-10-22 Fractional-Order Models for Nuclear Reactor Analysis presents fractional modeling issues in the context of anomalous diffusion processes in an accessible and practical way. The book emphasizes the importance of non-Fickian diffusion in heterogeneous systems as the core of the nuclear reactor, as well as different variations of diffusion processes in nuclear reactors which are presented to establish the importance of nuclear and thermohydraulic phenomena and the physical side effects of feedback. In addition, the book analyzes core issues in fractional modeling in nuclear reactors surrounding phenomenological description and important analytical sub-diffusive processes in the transport neutron. Users will find the most innovative modeling techniques of nuclear reactors using operator differentials of fractional order and applications in nuclear design and reactor dynamics. Proposed methods are tested with Boltzmann equations and non-linear order models alongside real data from nuclear power plants, making this a valuable resource for nuclear professionals, researchers and graduate students, as well as those working in nuclear research centers with expertise in mathematical modeling, physics and control. - Presents and analyzes a new paradigm of nuclear reactor phenomena with fractional modeling - Considers principles of fractional calculation, methods of solving differential equations of fractional order, and their applications - Includes methodologies of linear and nonlinear analysis, along with design and dynamic analyses |
calculus - Difference between functional and function.
The modern technical definition of a functional is a function from a vector space into the scalar field. For example, finding the length of a vector is a (non-linear) functional, or taking a vector …
Functional neurologic disorder/conversion disorder - Mayo Clinic
Jan 11, 2022 · Functional neurologic disorder is related to how the brain functions, rather than damage to the brain's structure (such as from a stroke, multiple sclerosis, infection or injury). …
Functional dyspepsia - Symptoms and causes - Mayo Clinic
Jan 4, 2025 · Functional dyspepsia is a term used to describe a lingering upset stomach that has no obvious cause. Functional dyspepsia (dis-PEP-see-uh) also is called nonulcer dyspepsia. …
Good book for self study of functional analysis
May 24, 2015 · Functional analysis is, for a large part, linear algebra on a infinite dimensional vector space over the real or complex numbers. Having a good intuition from linear algebra is …
Functional dyspepsia - Diagnosis and treatment - Mayo Clinic
Jan 4, 2025 · Functional dyspepsia that can't be managed with lifestyle changes may need treatment. Treatment depends on symptoms. It may combine medicines and behavior therapy. …
Functional neurologic disorder/conversion disorder - Mayo Clinic
Jan 11, 2022 · Spinal cord rehabilitation, Brain rehabilitation, Cancer rehabilitation, Spasticity therapy, Neurological rehabilitatio... n, Inpatient rehabilitation , Outpatient ...
Nonpharmacological approaches to management of functional ...
Feb 9, 2019 · Adult functional gastrointestinal disorders (FGIDs) are brain-gut interaction disorders that affect about 1 out of every 4 adults and have a significant negative impact on quality of life, …
Overview of basic facts about Cauchy functional equation
Also a few other equations related to this equation are often studied. (Equations which can be easily transformed to Cauchy functional equation or can be solved by using similar methods.) …
calculus of variations - What is the functional derivative ...
Apr 4, 2020 · notice that the RHS is equivalent to the functional derivative defined above. However, it is $$\frac{\delta F}{\delta \rho} (x)$$ that is defined to be the functional derivative, …
Functional analysis textbook (or course) with complete solutions to ...
Functional analysis is mostly not explicit (until the very end and even then it's bare bones) but it is informed by the functional analytic point of view throughout. Well, all of basic analysis (real, …
calculus - Difference between functional and function.
The modern technical definition of a functional is a function from a vector space into the scalar field. For example, finding the length of a vector is a (non-linear) functional, or taking a vector …
Functional neurologic disorder/conversion disorder - Mayo Clinic
Jan 11, 2022 · Functional neurologic disorder is related to how the brain functions, rather than damage to the brain's structure (such as from a stroke, multiple sclerosis, infection or injury). …
Functional dyspepsia - Symptoms and causes - Mayo Clinic
Jan 4, 2025 · Functional dyspepsia is a term used to describe a lingering upset stomach that has no obvious cause. Functional dyspepsia (dis-PEP-see-uh) also is called nonulcer dyspepsia. …
Good book for self study of functional analysis
May 24, 2015 · Functional analysis is, for a large part, linear algebra on a infinite dimensional vector space over the real or complex numbers. Having a good intuition from linear algebra is …
Functional dyspepsia - Diagnosis and treatment - Mayo Clinic
Jan 4, 2025 · Functional dyspepsia that can't be managed with lifestyle changes may need treatment. Treatment depends on symptoms. It may combine medicines and behavior therapy. …
Functional neurologic disorder/conversion disorder - Mayo Clinic
Jan 11, 2022 · Spinal cord rehabilitation, Brain rehabilitation, Cancer rehabilitation, Spasticity therapy, Neurological rehabilitatio... n, Inpatient rehabilitation , Outpatient ...
Nonpharmacological approaches to management of functional ...
Feb 9, 2019 · Adult functional gastrointestinal disorders (FGIDs) are brain-gut interaction disorders that affect about 1 out of every 4 adults and have a significant negative impact on …
Overview of basic facts about Cauchy functional equation
Also a few other equations related to this equation are often studied. (Equations which can be easily transformed to Cauchy functional equation or can be solved by using similar methods.) …
calculus of variations - What is the functional derivative ...
Apr 4, 2020 · notice that the RHS is equivalent to the functional derivative defined above. However, it is $$\frac{\delta F}{\delta \rho} (x)$$ that is defined to be the functional derivative, …
Functional analysis textbook (or course) with complete solutions to ...
Functional analysis is mostly not explicit (until the very end and even then it's bare bones) but it is informed by the functional analytic point of view throughout. Well, all of basic analysis (real, …
