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 Krakow, Poland, which was organized by the Faculty of Electrical Engineering, Automatics, Computer Science and Biomedical Engineering.

Synchronization of chaotic systems, a patently nonlinear phenomenon, has emerged as a highly active interdisciplinary research topic at the interface of physics, biology, applied mathematics and engineering sciences. In this connection, time-delay systems described by delay differential equations have developed as particularly
suitable tools for modeling specific dynamical systems. Indeed, time-delay is ubiquitous in many physical systems, for example due to finite
switching speeds of amplifiers in electronic circuits, finite lengths of vehicles in traffic flows, finite signal propagation times in biological networks and circuits, and quite generally whenever memory effects are relevant.
This monograph presents the basics of chaotic time-delay systems and their synchronization with an emphasis on the effects of time-delay feedback which give rise to new collective dynamics.
Special attention is devoted to scalar chaotic/hyperchaotic time-delay
systems, and some higher order models, occurring in different branches of science and technology as well as to the synchronization of their coupled versions.

Last but not least, the presentation as a whole strives for a balance between the necessary mathematical description of the basics
and the detailed presentation of real-world applications.

The "Turbulence and Interactions 2009" (TI2009) conference was held in Saint- Luce on the island of La Martinique, France, on May 31-June 5, 2009. The sci- tific sponsors of the conference were * DGA * Ecole Polytechnique Federale de Lausanne (EPFL), * ERCOFTAC : European Research Community on Flow, Turbulence and Combustion, * Institut Jean Le Rond d'Alembert, Paris, * ONERA. This second TI conference was very successful as it attracted 65 researchers from 17 countries. The magnificent venue and the beautiful weather helped the participants to discuss freely and casually, share ideas and projects, and spend very good times all together. The organisers were fortunate in obtaining the presence of the following - vited speakers: L. Fuchs (KTH, Stockholm and Lund University), J. Jimenez (Univ. Politecnica Madrid), C.-H. Moeng (NCAR), A. Scotti (University of North Carolina), L. Shen (Johns Hopkins University) and A.J. Smits (Princeton Univ- sity). The topics covered by the 62 contributed papers ranged from experimental results through theory to computations. They represent a snapshot of the state-- the-art in turbulence research. The papers of the conference went through the usual reviewing process and the result is given in this book of Proceedings. In the present volume, the reader will find the keynote lectures followed by the contributed talks given in alphabetical order of the first author.

Gathering the proceedings of the 12th CHAOS2019 International Conference, this book highlights recent developments in nonlinear, dynamical and complex systems. The conference was intended to provide an essential forum for Scientists and Engineers to exchange ideas, methods, and techniques in the field of Nonlinear Dynamics, Chaos, Fractals and their applications in General Science and the Engineering Sciences. The respective chapters address key methods, empirical data and computer techniques, as well as major theoretical advances in the applied nonlinear field. Beyond showcasing the state of the art, the book will help academic and industrial researchers alike apply chaotic theory in their studies.

The idea for this book originated during the workshop "Model order reduction, coupled problems and optimization" held at the Lorentz Center in Leiden from S- tember 19-23, 2005. During one of the discussion sessions, it became clear that a book describing the state of the art in model order reduction, starting from the very basics and containing an overview of all relevant techniques, would be of great use for students, young researchers starting in the ?eld, and experienced researchers. The observation that most of the theory on model order reduction is scattered over many good papers, making it dif?cult to ?nd a good starting point, was supported by most of the participants. Moreover, most of the speakers at the workshop were willing to contribute to the book that is now in front of you. The goal of this book, as de?ned during the discussion sessions at the workshop, is three-fold: ?rst, it should describe the basics of model order reduction. Second, both general and more specialized model order reduction techniques for linear and nonlinear systems should be covered, including the use of several related numerical techniques. Third, the use of model order reduction techniques in practical appli- tions and current research aspects should be discussed. We have organized the book according to these goals. In Part I, the rationale behind model order reduction is explained, and an overview of the most common methods is described.

The book gives an introduction to networked control systems and describes new modeling paradigms, analysis methods for event-driven, digitally networked systems, and design methods for distributed estimation and control. Networked model predictive control is developed as a means to tolerate time delays and packet loss brought about by the communication network. In event-based control the traditional periodic sampling is replaced by state-dependent triggering schemes. Novel methods for multi-agent systems ensure complete or clustered synchrony of agents with identical or with individual dynamics. The book includes numerous references to the most recent literature. Many methods are illustrated by numerical examples or experimental results.

The volume provides a comprehensive, up-to-date account on recent developments concerning the incorporation of fuzzy capabilities in Petri Net models. The results of such studies originated the class of models that have been designated by Fuzzy Petri Nets. The recent papers specially elaborated for this volume range over several aspects of fuzziness in Petri nets. They form an interesting collection of original works that covers a great variety of relevant problems concerning the concept of Fuzzy Petri Net model. The articles approach several of the most outstanding issues in the framework of Fuzzy Petri nets, such as the representation of time, consistency checking, learning, design, computational efficiency, modelling flexibility, among others. From the material collected in the book one can extract the points of view of leading researchers concerning the basic and advanced concepts, advantages, potential applications and open problems, related to the field.

This volume contains a selection of the most important papers in the theory of chaotic attractors over the past 40 years. It is dedicated to James Yorke - a pioneer in the field and a recipient of the 2003 Japan prize - on the occasion of his 60th birthday. The volume includes an introduction to Yorke's work and an overview of key developments in the theory of chaotic attractors.

This book contains contributions by some of the leading researchers in the area of grey systems theory and applications. All the papers included in this volume are selected from the contributions physically presented at the 2009 IEEE International Conference on Grey Systems and Intelligent Services, November 11 - 12, 2009, Nanjing, Jiangsu, People's Republic of China. This event was jointly sponsored by IEEE Systems, Man, and Cybernetics Society, Natural Science Foundation of China, and Grey Systems Society of China. Additionally, Nanjing University of Aeronautics and Astronautics also invested heavily in this event with its direct and indirect financial and administrative supports. The conference aimed at bringing together all scholars and experts in the fields of grey systems and intelligent services from around the world to share their cutting edge research results, exchange innovative ideas, promote mutual understanding, and seek potential opportunities for collaboration. The conference program c- mittee received 1054 full paper submissions from 16 countries and geographical regions. Nine hundred sixty four papers were submitted for regular sessions and 90 papers were tunnelled directly for special topic sessions. All the submitted papers, including those aiming at special topic sessions, were rigorously reviewed by at least 3 reviewers. Based on the reviewers' reports, 251 papers were accepted for oral presentations, while 99 accepted for poster presentations. In other words, only slightly over 33% of the submitted papers were accepted by this conference. The rate of acceptance was lower than one third of the total submissions.

This special volume is dedicated to Boris M. Mordukhovich, on the occasion of his 60th birthday, and aims to celebrate his fundamental contributionsto variational analysis, generalizeddifferentiationand their applications.A main exampleof these contributions is Boris' recent opus magnus "Variational Analysis and Generalized Differentiation"(vols. I and II) [2,3]. A detailed explanationand careful description of Boris' research and achievements can be found in [1]. Boris' active work and jovial attitude have constantly inspired researchers of several generations, with whom he has generously shared his knowledgeand ent- siasm, along with his well-known warmth and human touch. Variationalanalysis is a rapidlygrowing?eld within pure and applied mathem- ics, with numerous applications to optimization, control theory, economics, en- neering, and other disciplines. Each of the 12 chapters of this volume is a carefully reviewed paper in the ?eld of variational analysis and related topics. Many chapters of this volume were presented at the International Symposium on Variational Analysis and Optimization (ISVAO), held in the Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan, from November 28 to November 30, 2008. The symposium was organized in honour of Boris' 60thbirthday.It broughttogetherBorisandotherresearchersto discusssta- of-the-art results in variational analysis and its applications, with emphasis on op- mization and control. We thank the organizers and participants of the symposium, who made the symposium a highly bene?cial and enjoyable event. We are also grateful to all the authors of this special volume, who have taken the opportunityto celebrate Boris' birthdayand his decadesof contributionsto the area.

This book contains a selected collection of papers providing an overview of the state of the art in the study of dynamical systems. A broad range of aspects of dynamical systems is covered, focusing on discrete and continuous dynamical systems, bifurcation theory, celestial mechanics, delay difference and differential equations, Hamiltonian systems and also the classic challenges in planar vector fields. Particular attention has been posed on real-world applications of dynamical systems, showing the constant interaction of the field with other sciences. The authors have made a special effort in placing the reader at the frontiers of current knowledge in the discipline. In this way, recent advances and new trends become available. The papers are based on talks given at the International Conference Dynamical Systems: 100 years after Poincare held at the University of Oviedo, Gijon (Spain), on September 3-7, 2012. Recent advances and new trends have been discussed during the meeting, including applications to a wide range of disciplines such as Biology, Chemistry, Physics and Economics, among others. The memory of Poincare, who laid the foundations of dynamical systems, provided the backdrop for the discussion of the new challenges 100 years after his death.

Classical social choice theory relies heavily on the assumption that all individuals have fixed preference orderings. This highly original book presents a new theory of social preferences that explicitly accounts for important social phenomena such as coordination, compromise, negotiation and altruism. Drawing on cybernetics and network theory, it extends classical social choice theory by constructing a framework that allows for dynamic preferences that are modulated by the situation-dependent social influence that they exert on each other. In this way the book shows how members of a social network may modulate their preferences to account for social context. This important expansion of social choice theory will be of interest to readers in a wide variety of disciplines, including economists and political scientists concerned with choice theory as well as computer scientists and engineers working on network theory.

This book is devoted to a new branch of experimental design theory called simulation experimental design. There are many books devoted either to the theory of experimental design or to system simulation techniques, but in this book an approach to combine both fields is developed. Especially the mathematical theory of such universal variance reduction techniques as splitting and Russian Roulette is explored. The book contains a number of results on regression design theory related to nonlinear problems, the E-optimum criterion and designs which minimize bias. Audience: This volume will be of value to readers interested in systems simulation, applied statistics and numerical methods with basic knowledge of applied statistics and linear algebra.

This book presents the latest research on applications of artificial intelligence and the Internet of Things in renewable energy systems. Advanced renewable energy systems must necessarily involve the latest technology like artificial intelligence and Internet of Things to develop low cost, smart and efficient solutions. Intelligence allows the system to optimize the power, thereby making it a power efficient system; whereas, Internet of Things makes the system independent of wire and flexibility in operation. As a result, intelligent and IOT paradigms are finding increasing applications in the study of renewable energy systems. This book presents advanced applications of artificial intelligence and the internet of things in renewable energy systems development. It covers such topics as solar energy systems, electric vehicles etc. In all these areas applications of artificial intelligence methods such as artificial neural networks, genetic algorithms, fuzzy logic and a combination of the above, called hybrid systems, are included. The book is intended for a wide audience ranging from the undergraduate level up to the research academic and industrial communities engaged in the study and performance prediction of renewable energy systems.

This book addresses the processes of stochastic structure formation in two-dimensional geophysical fluid dynamics based on statistical analysis of Gaussian random fields, as well as stochastic structure formation in dynamic systems with parametric excitation of positive random fields f(r,t) described by partial differential equations. Further, the book considers two examples of stochastic structure formation in dynamic systems with parametric excitation in the presence of Gaussian pumping. In dynamic systems with parametric excitation in space and time, this type of structure formation either happens - or doesn't! However, if it occurs in space, then this almost always happens (exponentially quickly) in individual realizations with a unit probability. In the case considered, clustering of the field f(r,t) of any nature is a general feature of dynamic fields, and one may claim that structure formation is the Law of Nature for arbitrary random fields of such type. The study clarifies the conditions under which such structure formation takes place. To make the content more accessible, these conditions are described at a comparatively elementary mathematical level by employing ideas from statistical topography.

Geometrical Dynamics of Complex Systems is a graduate-level monographic textbook. Itrepresentsacomprehensiveintroductionintorigorousgeometrical dynamicsofcomplexsystemsofvariousnatures. By'complexsystems', inthis book are meant high-dimensional nonlinear systems, which can be (but not necessarily are) adaptive. This monograph proposes a uni?ed geometrical - proachtodynamicsofcomplexsystemsofvariouskinds: engineering, physical, biophysical, psychophysical, sociophysical, econophysical, etc. As their names suggest, all these multi-input multi-output (MIMO) systems have something in common: the underlying physics. However, instead of dealing with the pop- 1 ular 'soft complexity philosophy', we rather propose a rigorous geometrical and topological approach. We believe that our rigorous approach has much greater predictive power than the soft one. We argue that science and te- nology is all about prediction and control. Observation, understanding and explanation are important in education at undergraduate level, but after that it should be all prediction and control. The main objective of this book is to show that high-dimensional nonlinear systems and processes of 'real life' can be modelled and analyzed using rigorous mathematics, which enables their complete predictability and controllability, as if they were linear systems. It is well-known that linear systems, which are completely predictable and controllable by de?nition - live only in Euclidean spaces (of various - mensions). They are as simple as possible, mathematically elegant and fully elaborated from either scienti?c or engineering side. However, in nature, no- ing is linear. In reality, everything has a certain degree of nonlinearity, which means: unpredictability, with subsequent uncontrollability.

Control of Linear Parameter Varying Systems compiles state-of-the-art contributions on novel analytical and computational methods for addressing system identification, model reduction, performance analysis and feedback control design and addresses address theoretical developments, novel computational approaches and illustrative applications to various fields. Part I discusses modeling and system identification of linear parameter varying systems, Part II covers the importance of analysis and control design when working with linear parameter varying systems (LPVS) , Finally, Part III presents an applications based approach to linear parameter varying systems, including modeling of a turbocharged diesel engines, Multivariable control of wind turbines, modeling and control of aircraft engines, control of an autonomous underwater vehicles and analysis and synthesis of re-entry vehicles.

This book joins the multitude of Control Systems books now available, but is neither a textbook nor a monograph. Rather it may be described as a resource book or survey of the elements/essentials of feedback control systems. The material included is a result of my development, over a period of several years, of summaries written to supplement a number of standard textbooks for undergraduate and early post-graduate courses. Those notes, plus more work than I care right now to contemplate, are intended to be helpful both to students and to professional engineers. Too often, standard textbooks seem to overlook some of the engineering realities of (roughly) how much things cost or how big of hardware for computer programs for simple algorithms are, sensing and actuation, of special systems such as PLCs and PID controllers, of the engineering of real systems from coverage of SISO theories, and of the special characteristics of computers, their programming, and their potential interactions into systems. In particular, students with specializations other than control systems are not being exposed to the breadth of the considerations needed in control systems engineering, perhaps because it is assumed that they are always to be part of a multicourse sequence taken by specialists. The lectures given to introduce at least some of these aspects were more effective when supported by written material: hence, the need for my notes which preceded this book.

One of the most important tasks faced by decision-makers in business and government is that of selection. Selection problems are challenging in that they require the balancing of multiple, often conflicting, criteria. In recent years, a number of interesting decision aids have become available to assist in such decisions.
The aim of this book is to provide a comparative survey of many of the decision aids currently available. The first chapters present general ideas which underpin the methodologies used to design these aids. Subsequent chapters then focus on specific decision aids and demonstrate some of the software which implement these ideas. A final chapter provides a comparative analysis of their strengths and weaknesses.

Optimization, simulation and control play an increasingly important role in science and industry. Because of their numerous applications in various disciplines, research in these areas is accelerating at a rapid pace.

This volume brings together the latest developments in these areas of research as well as presents applications of these results to a wide range of real-world problems. The book is composed of invited contributions by experts from around the world who work to develop and apply new optimization, simulation and control techniques either at a theoretical level or in practice. Some key topics presented include: equilibrium problems, multi-objective optimization, variational inequalities, stochastic processes, numerical analysis, optimization in signal processing, and various other interdisciplinary applications.

This volume can serve as a useful resource for researchers, practitioners, and advanced graduate students of mathematics and engineering working in research areas where results in optimization, simulation and control can be applied.

'Rana el Kaliouby's vision for how technology should work in parallel with empathy is bold, inspired and hopeful' Arianna Huffington, founder and CEO of Thrive Global 'This lucid and captivating book by a renowned pioneer of emotion-AI tackles one of the most pressing issues of our time: How can we ensure a future where this technology empowers rather than surveils and manipulates us?' Max Tegmark, professor of physics at Massachusetts Institute of Technology and author of Life 3.0 We are entering an empathy crisis. Most of our communication is conveyed through non-verbal cues - facial expressions, tone of voice, body language - nuances that are completely lost when we interact through our smartphones and other technology. The result is a digital universe that's emotion-blind - a society lacking in empathy. Rana el Kaliouby discovered this when she left Cairo, a newly-married, Muslim woman, to take up her place at Cambridge University to study computer science. Many thousands of miles from home, she began to develop systems to help her better connect with her family. She started to pioneer the new field of Emotional Intelligence (EI). She now runs her company, Affectiva (the industry-leader in this emerging field) that builds EI into our technology and develops systems that understand humans the way we understand one another. In a captivating memoir, Girl Decoded chronicles el Kaliouby's mission to humanise technology and what she learns about humanity along the way.

This monograph contains an in-depth analysis of the dynamics given by a linear Hamiltonian system of general dimension with nonautonomous bounded and uniformly continuous coefficients, without other initial assumptions on time-recurrence. Particular attention is given to the oscillation properties of the solutions as well as to a spectral theory appropriate for such systems. The book contains extensions of results which are well known when the coefficients are autonomous or periodic, as well as in the nonautonomous two-dimensional case. However, a substantial part of the theory presented here is new even in those much simpler situations. The authors make systematic use of basic facts concerning Lagrange planes and symplectic matrices, and apply some fundamental methods of topological dynamics and ergodic theory. Among the tools used in the analysis, which include Lyapunov exponents, Weyl matrices, exponential dichotomy, and weak disconjugacy, a fundamental role is played by the rotation number for linear Hamiltonian systems of general dimension. The properties of all these objects form the basis for the study of several themes concerning linear-quadratic control problems, including the linear regulator property, the Kalman-Bucy filter, the infinite-horizon optimization problem, the nonautonomous version of the Yakubovich Frequency Theorem, and dissipativity in the Willems sense. The book will be useful for graduate students and researchers interested in nonautonomous differential equations; dynamical systems and ergodic theory; spectral theory of differential operators; and control theory.

This edited monograph provides a comprehensive and in-depth analysis of sliding mode control, focusing on event-triggered implementation. The technique allows to prefix the steady-state bounds of the system, and this is independent of any boundary disturbances. The idea of event-triggered SMC is developed for both single input / single output and multi-input / multi-output linear systems. Moreover, the reader learns how to apply this method to nonlinear systems. The book primarily addresses research experts in the field of sliding mode control, but the book may also be beneficial for graduate students.

"Takagi-Sugeno Fuzzy Systems Non-fragile H-infinity Filtering" investigates the problem of non-fragile H-infinity filter design for Takagi-Sugeno (T-S) fuzzy systems. Given a T-S fuzzy system, the objective of this book is to design an H-infinity filter with the gain variations such that the filtering error system guarantees a prescribed H-infinity performance level. Furthermore, it demonstrates that the solution of non-fragile H-infinity filter design problem can be obtained by solving a set of linear matrix inequalities (LMIs).
The intended audiences are graduate students and researchers bothfrom thefields of engineering and mathematics.
Dr. Xiao-Heng Chang is an Associate Professor at the College of Engineering, Bohai University, Jinzhou, Liaoning, China."