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.

This volume presents recent advances in the field of matrix analysis based on contributions at the MAT-TRIAD 2015 conference. Topics covered include interval linear algebra and computational complexity, Birkhoff polynomial basis, tensors, graphs, linear pencils, K-theory and statistic inference, showing the ubiquity of matrices in different mathematical areas. With a particular focus on matrix and operator theory, statistical models and computation, the International Conference on Matrix Analysis and its Applications 2015, held in Coimbra, Portugal, was the sixth in a series of conferences. Applied and Computational Matrix Analysis will appeal to graduate students and researchers in theoretical and applied mathematics, physics and engineering who are seeking an overview of recent problems and methods in matrix analysis.

This book, featuring a truly interdisciplinary approach, provides an overview of cutting-edge mathematical theories and techniques that promise to play a central role in climate science. It brings together some of the most interesting overview lectures given by the invited speakers at an important workshop held in Rome in 2013 as a part of MPE2013 ("Mathematics of Planet Earth 2013"). The aim of the workshop was to foster the interaction between climate scientists and mathematicians active in various fields linked to climate sciences, such as dynamical systems, partial differential equations, control theory, stochastic systems, and numerical analysis. Mathematics and statistics already play a central role in this area. Likewise, computer science must have a say in the efforts to simulate the Earth's environment on the unprecedented scale of petabytes. In the context of such complexity, new mathematical tools are needed to organize and simplify the approach. The growing importance of data assimilation techniques for climate modeling is amply illustrated in this volume, which also identifies important future challenges.

This book is devoted to the modeling and understanding of complex urban systems. This second volume of Understanding Complex Urban Systems focuses on the challenges of the modeling tools, concerning, e.g., the quality and quantity of data and the selection of an appropriate modeling approach. It is meant to support urban decision-makers-including municipal politicians, spatial planners, and citizen groups-in choosing an appropriate modeling approach for their particular modeling requirements. The contributors to this volume are from different disciplines, but all share the same goal: optimizing the representation of complex urban systems. They present and discuss a variety of approaches for dealing with data-availability problems and finding appropriate modeling approaches-and not only in terms of computer modeling. The selection of articles featured in this volume reflect a broad variety of new and established modeling approaches such as: - An argument for using Big Data methods in conjunction with Agent-based Modeling; - The introduction of a participatory approach involving citizens, in order to utilize an Agent-based Modeling approach to simulate urban-growth scenarios; - A presentation of semantic modeling to enable a flexible application of modeling methods and a flexible exchange of data; - An article about a nested-systems approach to analyzing a city's interdependent subsystems (according to these subsystems' different velocities of change); - An article about methods that use Luhmann's system theory to characterize cities as systems that are composed of flows; - An article that demonstrates how the Sen-Nussbaum Capabilities Approach can be used in urban systems to measure household well-being shifts that occur in response to the resettlement of urban households; - A final article that illustrates how Adaptive Cycles of Complex Adaptive Systems, as well as innovation, can be applied to gain a better understanding of cities and to promote more resilient and more sustainable urban futures.

This book offers advanced parallel and distributed algorithms and experimental laboratory prototypes of unconventional shortest path solvers. In addition, it presents novel and unique algorithms of solving shortest problems in massively parallel cellular automaton machines. The shortest path problem is a fundamental and classical problem in graph theory and computer science and is frequently applied in the contexts of transport and logistics, telecommunication networks, virtual reality and gaming, geometry, and social networks analysis. Software implementations include distance-vector algorithms for distributed path computation in dynamics networks, parallel solutions of the constrained shortest path problem, and application of the shortest path solutions in gathering robotic swarms. Massively parallel algorithms utilise cellular automata, where a shortest path is computed either via matrix multiplication in automaton arrays, or via the representation of data graphs in automaton lattices and using the propagation of wave-like patterns. Unconventional shortest path solvers are presented in computer models of foraging behaviour and protoplasmic network optimisation by the slime mould Physarum polycephalum and fluidic devices, while experimental laboratory prototypes of path solvers using chemical media, flows and droplets, and electrical current are also highlighted. The book will be a pleasure to explore for readers from all walks of life, from undergraduate students to university professors, from mathematicians, computers scientists and engineers to chemists and biologists.

This book focuses on the control of fractal behaviors in nonlinear dynamics systems, addressing both the principles and purposes of control. For fractals in different systems, it presents revealing studies on the theory and applications of control, reflecting a spectrum of different control methods used with engineering technology. As such, it will benefit researchers, engineers, and graduate students in fields of fractals, chaos, engineering, etc.

This book reports on the latest advances and applications of chaotic systems. It consists of 25 contributed chapters by experts who are specialized in the various topics addressed in this book. The chapters cover a broad range of topics of chaotic systems such as chaos, hyperchaos, jerk systems, hyperjerk systems, conservative and dissipative systems, circulant chaotic systems, multi-scroll chaotic systems, finance chaotic system, highly chaotic systems, chaos control, chaos synchronization, circuit realization and applications of chaos theory in secure communications, mobile robot, memristors, cellular neural networks, etc. Special importance was given to chapters offering practical solutions, modeling and novel control methods for the recent research problems in chaos theory. This book will serve as a reference book for graduate students and researchers with a basic knowledge of chaos theory and control systems. The resulting design procedures on the chaotic systems are emphasized using MATLAB software.

This thesis proposes a novel Model Predictive Control (MPC) strategy, which modifies the usual MPC cost function in order to achieve a desirable sparse actuation. It features an 1-regularised least squares loss function, in which the control error variance competes with the sum of input channels magnitude (or slew rate) over the whole horizon length. While standard control techniques lead to continuous movements of all actuators, this approach enables a selected subset of actuators to be used, the others being brought into play in exceptional circumstances. The same approach can also be used to obtain asynchronous actuator interventions, so that control actions are only taken in response to large disturbances. This thesis presents a straightforward and systematic approach to achieving these practical properties, which are ignored by mainstream control theory.

This book presents a theory as well as methods to understand and to purposively influence complex systems. It suggests a theory of complex systems as nested systems, i. e. systems that enclose other systems and that are simultaneously enclosed by even other systems. According to the theory presented, each enclosing system emerges through time from the generative activities of the systems they enclose. Systems are nested and often emerge unplanned, and every system of high dynamics is enclosed by a system of slower dynamics. An understanding of systems with faster dynamics, which are always guided by systems of slower dynamics, opens up not only new ways to understanding systems, but also to effectively influence them. The aim and subject of this book is to lay out these thoughts and explain their relevance to the purposive development of complex systems, which are exemplified in case studies from an urban system. The interested reader, who is not required to be familiar with system-theoretical concepts or with theories of emergence, will be guided through the development of a theory of emergent nested systems. The reader will also learn about new ways to influence the course of events - even though the course of events is, in principle, unpredictable, due to the ever-new emergence of real novelty.

This book addresses recent technological progress that has led to an increased complexity in many natural and artificial systems. The resulting complexity research due to the emergence of new properties and spatio-temporal interactions among a large number of system elements - and between the system and its environment - is the primary focus of this text. This volume is divided into three parts: Part one focuses on societal and ecological systems, Part two deals with approaches for understanding, modeling, predicting and mastering socio-technical systems, and Part three includes real-life examples. Each chapter has its own special features; it is a self-contained contribution of distinguished experts working on different fields of science and technology relevant to the study of complex systems. Advances in Complex Systems of Contemporary Reality: Societal, Environmental and Engineered Systems will provide postgraduate students, researchers and managers with qualitative and quantitative methods for handling the many features of complex contemporary reality.

This undergraduate text explores a variety of large-scale phenomena - global warming, ice ages, water, poverty - and uses these case studies as a motivation to explore nonlinear dynamics, power-law statistics, and complex systems. Although the detailed mathematical descriptions of these topics can be challenging, the consequences of a system being nonlinear, power-law, or complex are in fact quite accessible. This book blends a tutorial approach to the mathematical aspects of complex systems together with a complementary narrative on the global/ecological/societal implications of such systems. Nearly all engineering undergraduate courses focus on mathematics and systems which are small scale, linear, and Gaussian. Unfortunately there is not a single large-scale ecological or social phenomenon that is scalar, linear, and Gaussian. This book offers students insights to better understand the large-scale problems facing the world and to realize that these cannot be solved by a single, narrow academic field or perspective. Instead, the book seeks to emphasize understanding, concepts, and ideas, in a way that is mathematically rigorous, so that the concepts do not feel vague, but not so technical that the mathematics get in the way. The book is intended for undergraduate students in a technical domain such as engineering, computer science, physics, mathematics, and environmental studies.

The main theme of this book is recent progress in structure-preserving algorithms for solving initial value problems of oscillatory differential equations arising in a variety of research areas, such as astronomy, theoretical physics, electronics, quantum mechanics and engineering. It systematically describes the latest advances in the development of structure-preserving integrators for oscillatory differential equations, such as structure-preserving exponential integrators, functionally fitted energy-preserving integrators, exponential Fourier collocation methods, trigonometric collocation methods, and symmetric and arbitrarily high-order time-stepping methods. Most of the material presented here is drawn from the recent literature. Theoretical analysis of the newly developed schemes shows their advantages in the context of structure preservation. All the new methods introduced in this book are proven to be highly effective compared with the well-known codes in the scientific literature. This book also addresses challenging problems at the forefront of modern numerical analysis and presents a wide range of modern tools and techniques.

This book presents 29 invited articles written by participants of the International Workshop on Operator Theory and its Applications held in Chemnitz in 2017. The contributions include both expository essays and original research papers illustrating the diversity and beauty of insights gained by applying operator theory to concrete problems. The topics range from control theory, frame theory, Toeplitz and singular integral operators, Schroedinger, Dirac, and Kortweg-de Vries operators, Fourier integral operator zeta-functions, C*-algebras and Hilbert C*-modules to questions from harmonic analysis, Monte Carlo integration, Fibonacci Hamiltonians, and many more. The book offers researchers in operator theory open problems from applications that might stimulate their work and shows those from various applied fields, such as physics, engineering, or numerical mathematics how to use the potential of operator theory to tackle interesting practical problems.

The last decades have seen the emergence of Complex Networks as the language with which a wide range of complex phenomena in fields as diverse as Physics, Computer Science, and Medicine (to name just a few) can be properly described and understood. This book provides a view of the state of the art in this dynamic field and covers topics ranging from network controllability, social structure, online behavior, recommendation systems, and network structure. This book includes the peer-reviewed list of works presented at the 7th Workshop on Complex Networks CompleNet 2016 which was hosted by the Universite de Bourgogne, France, from March 23-25, 2016. The 28 carefully reviewed and selected contributions in this book address many topics related to complex networks and have been organized in seven major groups: (1) Theory of Complex Networks, (2) Multilayer networks, (3) Controllability of networks, (4) Algorithms for networks, (5) Community detection, (6) Dynamics and spreading phenomena on networks, (7) Applications of Networks.

The central theme of this book is the extent to which the structure of the free dynamical boundaries of a system controls the evolution of the system as a whole. Applying three orthogonal types of thinking - mathematical, constructivist and morphological, it illustrates these concepts using applications to selected problems from the social and life sciences, as well as economics. In a broader context, it introduces and reviews some modern mathematical approaches to the science of complex systems. Standard modeling approaches (based on non-linear differential equations, dynamic systems, graph theory, cellular automata, stochastic processes, or information theory) are suitable for studying local problems. However they cannot simultaneously take into account all the different facets and phenomena of a complex system, and new approaches are required to solve the challenging problem of correlations between phenomena at different levels and hierarchies, their self-organization and memory-evolutive aspects, the growth of additional structures and are ultimately required to explain why and how such complex systems can display both robustness and flexibility. This graduate-level text also addresses a broader interdisciplinary audience, keeping the mathematical level essentially uniform throughout the book, and involving only basic elements from calculus, algebra, geometry and systems theory.

This book examines discrete dynamical systems with memory-nonlinear systems that exist extensively in biological organisms and financial and economic organizations, and time-delay systems that can be discretized into the memorized, discrete dynamical systems. It book further discusses stability and bifurcations of time-delay dynamical systems that can be investigated through memorized dynamical systems as well as bifurcations of memorized nonlinear dynamical systems, discretization methods of time-delay systems, and periodic motions to chaos in nonlinear time-delay systems. The book helps readers find analytical solutions of MDS, change traditional perturbation analysis in time-delay systems, detect motion complexity and singularity in MDS; and determine stability, bifurcation, and chaos in any time-delay system.

The book introduces possibly the most compact, simple and physically understandable tool that can describe, explain, predict and design the widest set of phenomena in time-variant and nonlinear oscillations. The phenomena described include parametric resonances, combined resonances, instability of forced oscillations, synchronization, distributed parameter oscillation and flatter, parametric oscillation control, robustness of oscillations and many others. Although the realm of nonlinear oscillations is enormous, the book relies on the concept of minimum knowledge for maximum understanding. This unique tool is the method of stationarization, or one frequency approximation of parametric resonance problem analysis in linear time-variant dynamic systems. The book shows how this can explain periodic motion stability in stationary nonlinear dynamic systems, and reveals the link between the harmonic stationarization coefficients and describing functions. As such, the book speaks the language of control: transfer functions, frequency response, Nyquist plot, stability margins, etc. An understanding of the physics of stability loss is the basis for the design of new oscillation control methods for, several of which are presented in the book. These and all the other findings are illustrated by numerical examples, which can be easily reproduced by readers equipped with a basic simulation package like MATLAB with Simulink. The book offers a simple tool for all those travelling through the world of oscillations, helping them discover its hidden beauty. Researchers can use the method to uncover unknown aspects, and as a reference to compare it with other, for example, abstract mathematical means. Further, it provides engineers with a minimalistic but powerful instrument based on physically measurable variables to analyze and design oscillatory systems.

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 book develops a set of reference methods capable of modeling uncertainties existing in membership functions, and analyzing and synthesizing the interval type-2 fuzzy systems with desired performances. It also provides numerous simulation results for various examples, which fill certain gaps in this area of research and may serve as benchmark solutions for the readers. Interval type-2 T-S fuzzy models provide a convenient and flexible method for analysis and synthesis of complex nonlinear systems with uncertainties.

The book reports on the latest advances and applications of nonlinear control systems. It consists of 30 contributed chapters by subject experts who are specialized in the various topics addressed in this book. The special chapters have been brought out in the broad areas of nonlinear control systems such as robotics, nonlinear circuits, power systems, memristors, underwater vehicles, chemical processes, observer design, output regulation, backstepping control, sliding mode control, time-delayed control, variables structure control, robust adaptive control, fuzzy logic control, chaos, hyperchaos, jerk systems, hyperjerk systems, chaos control, chaos synchronization, etc. Special importance was given to chapters offering practical solutions, modeling and novel control methods for the recent research problems in nonlinear control systems. This book will serve as a reference book for graduate students and researchers with a basic knowledge of electrical and control systems engineering. The resulting design procedures on the nonlinear control systems are emphasized using MATLAB software.

This book is based on lectures from a one-year course at the Far Eastern Federal University (Vladivostok, Russia) as well as on workshops on optimal control offered to students at various mathematical departments at the university level. The main themes of the theory of linear and nonlinear systems are considered, including the basic problem of establishing the necessary and sufficient conditions of optimal processes. In the first part of the course, the theory of linear control systems is constructed on the basis of the separation theorem and the concept of a reachability set. The authors prove the closure of a reachability set in the class of piecewise continuous controls, and the problems of controllability, observability, identification, performance and terminal control are also considered. The second part of the course is devoted to nonlinear control systems. Using the method of variations and the Lagrange multipliers rule of nonlinear problems, the authors prove the Pontryagin maximum principle for problems with mobile ends of trajectories. Further exercises and a large number of additional tasks are provided for use as practical training in order for the reader to consolidate the theoretical material.

This book provides a description of advanced multi-agent and artificial intelligence technologies for the modeling and simulation of complex systems, as well as an overview of the latest scientific efforts in this field. A complex system features a large number of interacting components, whose aggregate activities are nonlinear and self-organized. A multi-agent system is a group or society of agents which interact with others cooperatively and/or competitively in order to reach their individual or common goals. Multi-agent systems are suitable for modeling and simulation of complex systems, which is difficult to accomplish using traditional computational approaches.

This book discusses recent advances in the estimation and control of networked systems with unacknowledged packet losses: systems usually known as user-datagram-protocol-like. It presents both the optimal and sub-optimal solutions in the form of algorithms, which are designed to be implemented easily by computer routines. It also provides MATLAB (R) routines for the key algorithms. It shows how these methods and algorithms can solve estimation and control problems effectively, and identifies potential research directions and ideas to help readers grasp the field more easily. The novel auxiliary estimator method, which is able to deal with estimators that consist of exponentially increasing terms, is developed to analyze the stability and convergence of the optimal estimator. The book also explores the structure and solvability of the optimal control, i.e. linear quadratic Gaussian control. It develops various sub-optimal but efficient solutions for estimation and control for industrial and practical applications, and analyzes their stability and performance. This is a valuable resource for researchers studying networked control systems, especially those related to non-TCP-like networks. The practicality of the ideas included makes it useful for engineers working with networked control.

This book presents the most important findings from the 9th International Conference on Modelling, Identification and Control (ICMIC'17), held in Kunming, China on July 10-12, 2017. It covers most aspects of modelling, identification, instrumentation, signal processing and control, with a particular focus on the applications of research in multi-agent systems, robotic systems, autonomous systems, complex systems, and renewable energy systems. The book gathers thirty comprehensively reviewed and extended contributions, which help to promote evolutionary computation, artificial intelligence, computation intelligence and soft computing techniques to enhance the safety, flexibility and efficiency of engineering systems. Taken together, they offer an ideal reference guide for researchers and engineers in the fields of electrical/electronic engineering, mechanical engineering and communication engineering.