The Dynamics of Control provides a carefully integrated development of the mathematical connections between nonlinear control, dynamical systems, and time-varying perturbed systems for scientists and engineers. The central theme is the notion of control flow with its global dynamics and linearization presented in detail.

The book's scope is comprehensive and includes global theory of dynamical systems under time-varying perturbations, global and local dynamics of control systems, connections between control systems and dynamical systems and the relevant numerical methods for global dynamics, linearization, and stability. Topics are developed with a diverse and extensive selection of applied problems from control and dynamical systems.

Topics and Features:

* complete coverage of unified theory of control flows

* wide array of motivating problems from control and dynamical systems to appeal to mathematicians, scientists, and engineers

* relevant motivation and a listing of important definitions and results at the beginning of each chapter

* a compilation of essential background information in four appendices: nonlinear geometric control, topological theory of dynamical systems, computations of reachable sets, and numerical solution of Hamiltona "Jacobia "Belman equations

* discussion of numerical methods

This new text and self-study reference guide is an excellent resource for the foundations and applications of control theory and nonlinear dynamics. All graduates, practitioners, and professionals in control theory, dynamical systems, perturbation theory, engineering, physics, and nonlinear dynamics will find the book a rich source of ideas, methods, andapplications.

The general topic of the symposium follows mechanisms development through all stages of conception, modeling, analysis, synthesis and control to advanced product design. This volume brings together the latest results in the field and celebrates a series of conferences that has been running for 40 years. The contributors and the editor are world leaders in their field.

Praise for the Series:
"This book will be a useful reference to control engineers and researchers. The papers contained cover well the recent advances in the field of modern control theory."
--IEEE Group Correspondence
"This book will help all those researchers who valiantly try to keep abreast of what is new in the theory and practice of optimal control."
--Control

The book is the first book on complex matrix equations including the conjugate of unknown matrices. The study of these conjugate matrix equations is motivated by the investigations on stabilization and model reference tracking control for discrete-time antilinear systems, which are a particular kind of complex system with structure constraints. It proposes useful approaches to obtain iterative solutions or explicit solutions for several types of complex conjugate matrix equation. It observes that there are some significant differences between the real/complex matrix equations and the complex conjugate matrix equations. For example, the solvability of a real Sylvester matrix equation can be characterized by matrix similarity; however, the solvability of the con-Sylvester matrix equation in complex conjugate form is related to the concept of con-similarity. In addition, the new concept of conjugate product for complex polynomial matrices is also proposed in order to establish a unified approach for solving a type of complex matrix equation.

1. MOTIVATION In many physical situations, a plant model is often provided with a qualitative or quantitative measure of associated model uncertainties. On the one hand, the validity of the model is guaranteed only inside a frequency band, so that nearly nothing can be said about the behavior of the real plant at high frequencies. On the other hand, if the model is derived on the basis of physical equations, it can be parameterized as a function of a few physical parameters, which are usually not perfectly known in practice. This is e.g. the case in aeronautical systems: as an example, the ae- dynamic model of an airplane is derived from the flight mechanics eq- tions. When synthesizing the aircraft control law, it is then necessary to take into account uncertainties in the values of the stability derivatives, which correspond to the physical coefficients of the aerodynamic model. Moreover, this airplane model does not perfectly represent the be- vior of the real aircraft. As a simple example, the flight control system or the autopilot are usually synthesized just using the aerodynamic model, thus without accounting for the flexible mechanicalstructure: the c- responding dynamics are indeed considered as high frequency neglected 1 dynamics, with respect to the dynamics of the rigid model .

This significantly revised edition presents a broad introduction to Control Systems and balances new, modern methods with the more classical. It is an excellent text for use as a first course in Control Systems by undergraduate students in all branches of engineering and applied mathematics. The book contains: A comprehensive coverage of automatic control, integrating digital and computer control techniques and their implementations, the practical issues and problems in Control System design; the three-term PID controller, the most widely used controller in industry today; numerous in-chapter worked examples and end-of-chapter exercises. This second edition also includes an introductory guide to some more recent developments, namely fuzzy logic control and neural networks.

Due to the rapid increase in readily available computing power, a corre sponding increase in the complexity of problems being tackled has occurred in the field of systems as a whole. A plethora of new methods which can be used on the problems has also arisen with a constant desire to deal with more and more difficult applications. Unfortunately by increasing the ac curacy in models employed along with the use of appropriate algorithms with related features, the resultant necessary computations can often be of very high dimension. This brings with it a whole new breed of problem which has come to be known as "The Curse of Dimensionality" . The expression "Curse of Dimensionality" can be in fact traced back to Richard Bellman in the 1960's. However, it is only in the last few years that it has taken on a widespread practical significance although the term di mensionality does not have a unique precise meaning and is being used in a slightly different way in the context of algorithmic and stochastic complex ity theory or in every day engineering. In principle the dimensionality of a problem depends on three factors: on the engineering system (subject), on the concrete task to be solved and on the available resources. A system is of high dimension if it contains a lot of elements/variables and/or the rela tionship/connection between the elements/variables is complicated."

This book, written by experts in the field, is based on the latest research on the analysis and synthesis of switched time-delay systems. It covers the stability, filtering, fault detection and control problems, which are studied using the average dwell time approach. It presents both the continuous-time and discrete-time systems and provides useful insights and methods, as well as practical algorithms that can be considered in other complex systems, such as neuron networks and genetic regulatory networks, making it a valuable resource for researchers, scientists and engineers in the field of system sciences and control communities.

This book covers the conventional and most recent theories and applications in the area of evolutionary algorithms, swarm intelligence, and meta-heuristics. Each chapter offers a comprehensive description of a specific algorithm, from the mathematical model to its practical application. Different kind of optimization problems are solved in this book, including those related to path planning, image processing, hand gesture detection, among others. All in all, the book offers a tutorial on how to design, adapt, and evaluate evolutionary algorithms. Source codes for most of the proposed techniques have been included as supplementary materials on a dedicated webpage.

Covers advances in the field of computer techniques and algorithms in digital signal processing.

Praise for Previous Volumes
"This book will be a useful reference to control engineers and researchers. The papers contained cover well the recent advances in the field of modern control theory."
-IEEE GROUP CORRESPONDANCE
"This book will help all those researchers who valiantly try to keep abreast of what is new in the theory and practice of optimal control."
-CONTROL

Adaptive Control provides techniques for the automatic adjustment in real time of controller parameters. Their purpose is to achieve or maintain a desired level of system performance when process parameters are unknown or variable. Such techniques operate by extracting significative information from real data in order to tune the controller and they feature a mechanism for adjusting parameters. The book explores both established ideas and recent trends in the field of adaptive control. More specifically, the book covers synthesis and analysis of parameter adaptation algorithms, robust digital control and recursive digital control in open and closed loop. This book considers the problems and seeks to find answers using mathematical sequences.To guide the reader, the book contains various applications of adaptive control techniques.

With contributions by specialists in optimization and practitioners in the fields of aerospace engineering, chemical engineering, and fluid and solid mechanics, the major themes include an assessment of the state of the art in optimization algorithms as well as challenging applications in design and control, in the areas of process engineering and systems with partial differential equation models.

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 Chapter 3 Flexible Neural Networks . . . . . . . . . . . . . . . . . . . . . . . . 61 3. 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 3. 2 Flexible Unipolar Sigmoid Functions . . . . . . . . . . . . . . . . . . . . . . . . . . 62 3. 3 Flexible Bipolar Sigmoid Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 3. 4 Learning Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 3. 4. 1 Generalized learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 3. 4. 2 Specialized learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3. 5 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 3. 6 Combinations of Flexible Artificial Neural Network Topologies . . . . 79 3. 7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 Chapter 4 Self-Tuning PID Control 85 4. 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 4. 2 PID Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 4. 3 Flexible Neural Network as an Indirect Controller . . . . . . . . . . . . . . . 91 4. 4 Self-tunig PID Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 4. 5 Simulation Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 4. 5. 1 The Tank model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 4. 5. 2 Simulation study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 4. 5. 3 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 4. 6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 Chapter 5 Self-Tuning Computed Torque Control: Part I 107 5. 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 5. 2 Manipulator Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 5. 3 Computed Torque Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 5. 4 Self-tunig Computed Torque Control . . . . . . . . . . . . . . . . . . . . . . . . . 111 5. 5 Simulation Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 5. 5. 1 Simultaneous learning of connection weights and SF para- ters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 5. 5. 2 Learning of the sigmoid function parameters . . . . . . . . . . . . . 123 Vll 5. 5. 3 Simultaneous learning of SF parameters and output gains 129 5. 6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 Chapter 6 Self-Tuning Computed Torque Control: Part II 137 6. 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 6. 2 Simplification of Flexible Neural Networks . . . . . . . . . . . . . . . . . . . . 138 6. 3 Simulation Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 6. 3. 1 Simultaneous learning of connection weights and sigmoid function parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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

A predictive control algorithm uses a model of the controlled system to predict the system behavior for various input scenarios and determines the most appropriate inputs accordingly. Predictive controllers are suitable for a wide range of systems; therefore, their advantages are especially evident when dealing with relatively complex systems, such as nonlinear, constrained, hybrid, multivariate systems etc. However, designing a predictive control strategy for a complex system is generally a difficult task, because all relevant dynamical phenomena have to be considered. Establishing a suitable model of the system is an essential part of predictive control design. Classic modeling and identification approaches based on linear-systems theory are generally inappropriate for complex systems; hence, models that are able to appropriately consider complex dynamical properties have to be employed in a predictive control algorithm. This book first introduces some modeling frameworks, which can encompass the most frequently encountered complex dynamical phenomena and are practically applicable in the proposed predictive control approaches. Furthermore, unsupervised learning methods that can be used for complex-system identification are treated. Finally, several useful predictive control algorithms for complex systems are proposed and their particular advantages and drawbacks are discussed. The presented modeling, identification and control approaches are complemented by illustrative examples. The book is aimed towards researches and postgraduate students interested in modeling, identification and control, as well as towards control engineers needing practically usable advanced control methods for complex systems.

The scope of opportunities in chemical and biomolecular engineering has grown tremendously in recent years. Careers in Chemical and Biomolecular Engineering conveys the breadth and depth of today's chemical and biomolecular engineering practice, and describes the intellectually enriching, socially conscious and financially lucrative opportunities available for such graduates in an ever-widening array of industries and applications. This book aims to help students interested in studying chemical engineering and biomolecular engineering to understand the many potential career pathways that are available in these dynamic fields - and is an indispensable resource for the parents, teachers, advisors and guidance counselors who support them, In addition to 10 chapters that discuss the roles such graduates play in many diverse industries, this book also features 25 Profile articles that share in-depth, first-person insight from industry-leading chemical and biomolecular engineers. These technical professionals discuss their work and educational experiences (in terms of both triumphs and challenges), and share wisdom and recommendations for students pursuing these two dynamic engineering disciplines.

Precision Nanometrology describes the new field of precision nanometrology, which plays an important part in nanoscale manufacturing of semiconductors, optical elements, precision parts and similar items. It pays particular attention to the measurement of surface forms of precision workpieces and to stage motions of precision machines. The first half of the book is dedicated to the description of optical sensors for the measurement of angle and displacement, which are fundamental quantities for precision nanometrology. The second half presents a number of scanning-type measuring systems for surface forms and stage motions. The systems discussed include: * error separation algorithms and systems for measurement of straightness and roundness, * the measurement of micro-aspherics, * systems based on scanning probe microscopy, and * scanning image-sensor systems. Precision Nanometrology presents the fundamental and practical technologies of precision nanometrology with a helpful selection of algorithms, instruments and experimental data. It will be beneficial for researchers, engineers and postgraduate students involved in precision engineering, nanotechnology and manufacturing.

Inverse problems and optimal design have come of age as a consequence of the availability of better, more accurate, and more efficient simulation packages. Many of these simulators, which can run on small workstations, can capture the complicated behavior of the physical systems they are modeling, and have become commonplace tools in engineering and science. There is a great desire to use them as part of a process by which measured field data are analyzed or by which design of a product is automated. A major obstacle in doing precisely this is that one is ultimately confronted with a large-scale optimization problem. This volume contains expository articles on both inverse problems and design problems formulated as optimization. Each paper describes the physical problem in some detail and is meant to be accessible to researchers in optimization as well as those who work in applied areas where optimization is a key tool. What emerges in the presentations is that there are features about the problem that must be taken into account in posing the objective function, and in choosing an optimization strategy. In particular there are certain structures peculiar to the problems that deserve special treatment, and there is ample opportunity for parallel computation. THIS IS BACK COVER TEXT Inverse problems and optimal design have come of age as a consequence of the availability of better, more accurate, and more efficient, simulation packages. The problem of determining the parameters of a physical system from

The key attribute of a Fault Tolerant Control (FTC) system is its ability to maintain overall system stability and acceptable performance in the face of faults and failures within the feedback system. In this book Integral Sliding Mode (ISM) Control Allocation (CA) schemes for FTC are described, which have the potential to maintain close to nominal fault-free performance (for the entire system response), in the face of actuator faults and even complete failures of certain actuators. Broadly an ISM controller based around a model of the plant with the aim of creating a nonlinear fault tolerant feedback controller whose closed-loop performance is established during the design process. The second approach involves retro-fitting an ISM scheme to an existing feedback controller to introduce fault tolerance. This may be advantageous from an industrial perspective, because fault tolerance can be introduced without changing the existing control loops. A high fidelity benchmark model of a large transport aircraft is used to demonstrate the efficacy of the FTC schemes. In particular a scheme based on an LPV representation has been implemented and tested on a motion flight simulator.

This book introduces advanced thyristor-based shunt hybrid active power filters (HAPFs) for power quality improvement in power grids, which are characterized by a low dc-link operating voltage and a wide compensation range. This means they can overcome the high dc-link voltage requirement of conventional active power filters and the narrow compensation range problem of LC-coupling hybrid active power filters. Consisting of 10 chapters, the book discusses the principle, design, control and hardware implementation of thyristor-based hybrid active power filters. It covers 1) V-I characteristics, cost analysis, power loss and reliability studies of different power filters; 2) mitigation of the harmonic injection technique for thyristor-controlled parts; 3) nonlinear pulse width modulation (PWM) control; 4) parameter design methods; 5) minimum inverter capacity design; 6) adaptive dc-link voltage control; 7) unbalanced control strategy; 8) selective compensation techniques; and 9) the hardware prototype design of thyristor-based HAPFs, verified by simulation and experimental results. It enables readers to gain an understanding of the basic power electronics techniques applied in power systems as well as the advanced techniques for controlling, implementing and designing advanced thyristor-based HAPFs.

With contributions by specialists in optimization and practitioners in the fields of aerospace engineering, chemical engineering, and fluid and solid mechanics, the major themes include an assessment of the state of the art in optimization algorithms as well as challenging applications in design and control, in the areas of process engineering and systems with partial differential equation models.

This book aims at addressing the challenges of contemporary manufacturing in Industry 4.0 environment and future manufacturing (aka Industry 5.0), by implementing soft computing as one of the major sub-fields of artificial intelligence. It contributes to development and application of the soft computing systems, including links to hardware, software and enterprise systems, in resolving modern manufacturing issues in complex, highly dynamic and globalized industrial circumstances. It embraces heterogeneous complementary aspects, such as control, monitoring and modeling of different manufacturing tasks, including intelligent robotic systems and processes, addressed by various machine learning and fuzzy techniques; modeling and parametric optimization of advanced conventional and non-conventional, eco-friendly manufacturing processes by using machine learning and evolutionary computing techniques; cybersecurity framework for Internet of Things-based systems addressing trustworthiness and resilience in machine-to-machine and human-machine collaboration; static and dynamic digital twins integration and synchronization in a smart factory environment; STEP-NC technology for a smart machine vision system, and integration of Open CNC with Service-Oriented Architecture for STEP-NC monitoring system in a smart manufacturing. Areas of interest include but are not limited to applications of soft computing to address the following: dynamic process/system modeling and simulation, dynamic process/system parametric optimization, dynamic planning and scheduling, smart, predictive maintenance, intelligent and autonomous systems, improved machine cognition, effective digital twins integration, human-machine collaboration, robots, and cobots.

The solution of eigenvalue problems is an integral part of many scientific computations. For example, the numerical solution of problems in structural dynamics, electrical networks, macro-economics, quantum chemistry, and c- trol theory often requires solving eigenvalue problems. The coefficient matrix of the eigenvalue problem may be small to medium sized and dense, or large and sparse (containing many zeroelements). In the past tremendous advances have been achieved in the solution methods for symmetric eigenvalue pr- lems. The state of the art for nonsymmetric problems is not so advanced; nonsymmetric eigenvalue problems can be hopelessly difficult to solve in some situations due, for example, to poor conditioning. Good numerical algorithms for nonsymmetric eigenvalue problems also tend to be far more complex than their symmetric counterparts. This book deals with methods for solving a special nonsymmetric eig- value problem; the symplectic eigenvalue problem. The symplectic eigenvalue problem is helpful, e.g., in analyzing a number of different questions that arise in linear control theory for discrete-time systems. Certain quadratic eigenvalue problems arising, e.g., in finite element discretization in structural analysis, in acoustic simulation of poro-elastic materials, or in the elastic deformation of anisotropic materials can also lead to symplectic eigenvalue problems. The problem appears in other applications as well.

Conceived by Count Jacopo Francesco Riccati more than a quarter of a millennium ago, the Riccati equation has been widely studied in the subsequent centuries. Since its introduction in control theory in the sixties, the matrix Riccati equation has known an impressive range of applications, such as optimal control, H? optimization and robust stabilization, stochastic realization, synthesis of linear passive networks, to name but a few. This book consists of 11 chapters surveying the main concepts and results related to the matrix Riccati equation, both in continuous and discrete time. Theory, applications and numerical algorithms are extensively presented in an expository way. As a foreword, the history and prehistory of the Riccati equation is concisely presented.