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| singular perturbation methods in control analysis and design: Singular Perturbation Methods in Control Petar Kokotovic, Hassan K. Khali, John O'Reilly, 1999-01-01 This SIAM Classics edition of the 1986 book provides the theoretical foundation for representative control applications. |
| singular perturbation methods in control analysis and design: Singular Perturbation Methods in Control Petar V. Kokotović, Hassan K. Khalil, John O'Reilly, 1986 In this book, control theory merges with singular perturbation techniques to form the first comprehensive two-time-scale methodology for the modeling, analysis and design of control systems. Its goal is to simplify the software and hardware implementation of control algorithms, while improving their robustness properties. The text is intended for control engineers and graduate students who seek an introduction to singular perturbation methods in control. A feature of the book is the illustration of two-time-scale analysis and design procedures by way of case studies drawn from flight control, power systems and adaptive control. |
| singular perturbation methods in control analysis and design: Singular Perturbation Methods in Control Petar V. Kokotovic, 1999 |
| singular perturbation methods in control analysis and design: Singular Perturbation Methodology in Control Systems Desineni S. Naidu, 1988 This book presents the twin topics of singular perturbation methods and time scale analysis to problems in systems and control. The heart of the book is the singularly perturbed optimal control systems, which are notorious for demanding excessive computational costs. The book addresses both continuous control systems (described by differential equations) and discrete control systems (characterised by difference equations). |
| singular perturbation methods in control analysis and design: Singular Perturbation Methods in Control Petar Kokotovic, Hassan K. Khalil, John O'Reilly, 1999-01-01 Singular perturbations and time-scale techniques were introduced to control engineering in the late 1960s and have since become common tools for the modeling, analysis, and design of control systems. In this SIAM Classics edition of the 1986 book, the original text is reprinted in its entirety (along with a new preface), providing once again the theoretical foundation for representative control applications. This book continues to be essential in many ways. It lays down the foundation of singular perturbation theory for linear and nonlinear systems, it presents the methodology in a pedagogical way that is not available anywhere else, and it illustrates the theory with many solved examples, including various physical examples and applications. So while new developments may go beyond the topics covered in this book, they are still based on the methodology described here, which continues to be their common starting point. |
| singular perturbation methods in control analysis and design: Nonlinear Systems Analysis M. Vidyasagar, 2002-01-01 When M. Vidyasagar wrote the first edition of Nonlinear Systems Analysis, most control theorists considered the subject of nonlinear systems a mystery. Since then, advances in the application of differential geometric methods to nonlinear analysis have matured to a stage where every control theorist needs to possess knowledge of the basic techniques because virtually all physical systems are nonlinear in nature. The second edition, now republished in SIAM's Classics in Applied Mathematics series, provides a rigorous mathematical analysis of the behavior of nonlinear control systems under a variety of situations. It develops nonlinear generalizations of a large number of techniques and methods widely used in linear control theory. The book contains three extensive chapters devoted to the key topics of Lyapunov stability, input-output stability, and the treatment of differential geometric control theory. Audience: this text is designed for use at the graduate level in the area of nonlinear systems and as a resource for professional researchers and practitioners working in areas such as robotics, spacecraft control, motor control, and power systems. |
| singular perturbation methods in control analysis and design: Mathematics Applied to Deterministic Problems in the Natural Sciences C. C. Lin, L. A. Segel, 1988-12-01 This book addresses the construction, analysis, and intepretation of mathematical models that shed light on significant problems in the physical sciences, with exercises that reinforce, test and extend the reader's understanding. It may be used as an upper level undergraduate or graduate textbook as well as a reference for researchers. |
| singular perturbation methods in control analysis and design: Ergodicity, Stabilization, and Singular Perturbations for Bellman-Isaacs Equations Olivier Alvarez, Martino Bardi, 2010 Volume 204, number 960 (fourth of 5 numbers). |
| singular perturbation methods in control analysis and design: Perturbations James A. Murdock, 1999-01-01 Perturbations: Theory and Methods gives a thorough introduction to both regular and singular perturbation methods for algebraic and differential equations. Unlike most introductory books on the subject, this one distinguishes between formal and rigorous asymptotic validity, which are commonly confused in books that treat perturbation theory as a bag of heuristic tricks with no foundation. The meaning of uniformity is carefully explained in a variety of contexts. All standard methods, such as rescaling, multiple scales, averaging, matching, and the WKB method are covered, and the asymptotic validity (in the rigorous sense) of each method is carefully proved. First published in 1991, this book is still useful today because it is an introduction. It combines perturbation results with those known through other methods. Sometimes a geometrical result (such as the existence of a periodic solution) is rigorously deduced from a perturbation result, and at other times a knowledge of the geometry of the solutions is used to aid in the selection of an effective perturbation method. Dr. Murdock's approach differs from other introductory texts because he attempts to present perturbation theory as a natural part of a larger whole, the mathematical theory of differential equations. He explores the meaning of the results and their connections to other ways of studying the same problems. |
| singular perturbation methods in control analysis and design: Design of Nonlinear Control Systems with the Highest Derivative in Feedback Valery D. Yurkevich, 2004 This unique book presents an analytical uniform design methodology of continuous-time or discrete-time nonlinear control system design which guarantees desired transient performances in the presence of plant parameter variations and unknown external disturbances. All results are illustrated with numerical simulations, their practical importance is highlighted, and they may be used for real-time control system design in robotics, mechatronics, chemical reactors, electrical and electro-mechanical systems as well as aircraft control systems. The book is easy reading and is suitable for teaching. |
| singular perturbation methods in control analysis and design: Canard Cycles Peter De Maesschalck, Freddy Dumortier, Robert Roussarie, 2021-08-07 This book offers the first systematic account of canard cycles, an intriguing phenomenon in the study of ordinary differential equations. The canard cycles are treated in the general context of slow-fast families of two-dimensional vector fields. The central question of controlling the limit cycles is addressed in detail and strong results are presented with complete proofs. In particular, the book provides a detailed study of the structure of the transitions near the critical set of non-isolated singularities. This leads to precise results on the limit cycles and their bifurcations, including the so-called canard phenomenon and canard explosion. The book also provides a solid basis for the use of asymptotic techniques. It gives a clear understanding of notions like inner and outer solutions, describing their relation and precise structure. The first part of the book provides a thorough introduction to slow-fast systems, suitable for graduate students. The second and third parts will be of interest to both pure mathematicians working on theoretical questions such as Hilbert's 16th problem, as well as to a wide range of applied mathematicians looking for a detailed understanding of two-scale models found in electrical circuits, population dynamics, ecological models, cellular (FitzHugh–Nagumo) models, epidemiological models, chemical reactions, mechanical oscillators with friction, climate models, and many other models with tipping points. |
| singular perturbation methods in control analysis and design: Singularly Perturbed Boundary-Value Problems Luminita Barbu, Gheorghe Morosanu, 2007-12-14 This book offers a detailed asymptotic analysis of some important classes of singularly perturbed boundary value problems which are mathematical models for phenomena in biology, chemistry, and engineering. The authors are particularly interested in nonlinear problems, which have gone little-examined so far in literature dedicated to singular perturbations. The treatment presented here combines successful results from functional analysis, singular perturbation theory, partial differential equations, and evolution equations. |
| singular perturbation methods in control analysis and design: Design of Modern Control Systems David John Bell, Peter A. Cook, N. Munro, Institution of Electrical Engineers, 1982 The book reviews developments in the following fields: state-space theory; complex variable methods in feedback system analysis and design; robustness in variable control system design; design study using the characteristic locus method; inverse Nyquist array design method; nuclear boiler control scheme analysis and design; optimal control; control system design via mathematical programming; multivariable design optimisation; pole assignment; nonlinear systems; DDC system design; robust controller design; distributed parameter system control; and decentralised control. |
| singular perturbation methods in control analysis and design: Fitted Numerical Methods For Singular Perturbation Problems: Error Estimates In The Maximum Norm For Linear Problems In One And Two Dimensions (Revised Edition) John J H Miller, Eugene O'riordan, G I Shishkin, 2012-02-29 Since the first edition of this book, the literature on fitted mesh methods for singularly perturbed problems has expanded significantly. Over the intervening years, fitted meshes have been shown to be effective for an extensive set of singularly perturbed partial differential equations. In the revised version of this book, the reader will find an introduction to the basic theory associated with fitted numerical methods for singularly perturbed differential equations. Fitted mesh methods focus on the appropriate distribution of the mesh points for singularly perturbed problems. The global errors in the numerical approximations are measured in the pointwise maximum norm. The fitted mesh algorithm is particularly simple to implement in practice, but the theory of why these numerical methods work is far from simple. This book can be used as an introductory text to the theory underpinning fitted mesh methods. |
| singular perturbation methods in control analysis and design: Introduction to Singular Perturbations Robert E. Jr. O'Malley, 2012-12-02 Introduction to Singular Perturbations provides an overview of the fundamental techniques for obtaining asymptomatic solutions to boundary value problems. This text explores singular perturbation techniques, which are among the basic tools of several applied scientists. This book is organized into eight chapters, wherein Chapter 1 discusses the method of matched asymptomatic expansions, which has been frequently applied to several physical problems involving singular perturbations. Chapter 2 considers the nonlinear initial value problem to illustrate the regular perturbation method, and Chapter 3 explains how to construct asymptotic solutions for general linear equations. Chapter 4 discusses scalar equations and nonlinear system, whereas Chapters 5 and 6 explain the contrasts for initial value problems where the outer expansion cannot be determined without obtaining the initial values of the boundary layer correction. Chapters 7 and 8 deal with boundary value problem that arises in the study of adiabatic tubular chemical flow reactors with axial diffusion. This monograph is a valuable resource for applied mathematicians, engineers, researchers, students, and readers whose interests span a variety of fields. |
| singular perturbation methods in control analysis and design: Discrete-Time Control System Design with Applications C.A. Rabbath, N. Léchevin, 2013-12-02 This unique book provides a bridge between digital control theory and vehicle guidance and control practice. It presents practical techniques of digital redesign and direct discrete-time design suitable for a real-time implementation of controllers and guidance laws at multiple rates and with and computational techniques. The theory of digital control is given as theorems, lemmas, and propositions. The design of the digital guidance and control systems is illustrated by means of step-by-step procedures, algorithms, and case studies. The systems proposed are applied to realistic models of unmanned systems and missiles, and digital implementation. |
| singular perturbation methods in control analysis and design: Optimal Control Of Singularly Perturbed Linear Systems And Applications Zoran Gajic, 2001-01-04 Highlights the Hamiltonian approach to singularly perturbed linear optimal control systems. Develops parallel algorithms in independent slow and fast time scales for solving various optimal linear control and filtering problems in standard and nonstandard singularly perturbed systems, continuous- and discrete-time, deterministic and stochastic, mul |
| singular perturbation methods in control analysis and design: Introduction to Perturbation Techniques Ali H. Nayfeh, 2011-04-08 Similarities, differences, advantages and limitations of perturbation techniques are pointed out concisely. The techniques are described by means of examples that consist mainly of algebraic and ordinary differential equations. Each chapter contains a number of exercises. |
| singular perturbation methods in control analysis and design: Applied Optimal Control A. E. Bryson, 1975-01-01 This best-selling text focuses on the analysis and design of complicated dynamics systems. CHOICE called it “a high-level, concise book that could well be used as a reference by engineers, applied mathematicians, and undergraduates. The format is good, the presentation clear, the diagrams instructive, the examples and problems helpful...References and a multiple-choice examination are included.” |
| singular perturbation methods in control analysis and design: Control System Design Bernard Friedland, 2012-03-08 Introduction to state-space methods covers feedback control; state-space representation of dynamic systems and dynamics of linear systems; frequency-domain analysis; controllability and observability; shaping the dynamic response; more. 1986 edition. |
| singular perturbation methods in control analysis and design: Topological Methods For Set-valued Nonlinear Analysis Enayet U Tarafdar, Mohammad S R Chowdhury, 2008-02-22 This book provides a comprehensive overview of the authors' pioneering contributions to nonlinear set-valued analysis by topological methods. The coverage includes fixed point theory, degree theory, the KKM principle, variational inequality theory, the Nash equilibrium point in mathematical economics, the Pareto optimum in optimization, and applications to best approximation theory, partial equations and boundary value problems.Self-contained and unified in presentation, the book considers the existence of equilibrium points of abstract economics in topological vector spaces from the viewpoint of Ky Fan minimax inequalities. It also provides the latest developments in KKM theory and degree theory for nonlinear set-valued mappings. |
| singular perturbation methods in control analysis and design: Linear Systems Theory Ben M. Chen, Zongli Lin, Yacov Shamash, 2012-12-06 Structural properties play an important role in our understanding of linear systems in the state space representation. The structural canonical form representation of linear systems not only reveals the structural properties but also facilitates the design of feedback laws that meet various control objectives. In particular, it decomposes the system into various subsystems. These subsystems, along with the interconnections that exist among them, clearly show the structural properties of the system. The simplicity of the subsystems and their explicit interconnections with each other lead us to a deeper insight into how feedback control would take effect on the system, and thus to the explicit construction of feedback laws that meet our design specifications. The discovery of structural canonical forms and their applications in feedback design for various performance specifications has been an active area of research for a long time. The effectiveness of the structural decomposition approach has also been extensively explored in nonlinear systems and control theory in the recent past. The aim of this book is to systematically present various canonical represen tations of the linear system, that explicitly reveal different structural properties of the system, and to report on some recent developments on its utilization in sys tem analysis and design. |
| singular perturbation methods in control analysis and design: Multivariable Feedback Control: Analysis and Design Sigurd Skogestad, 2014 |
| singular perturbation methods in control analysis and design: Feedback Control Theory John Comstock Doyle, Bruce A. Francis, Allen Tannenbaum, 2009 An excellent introduction to feedback control system design, this book offers a theoretical approach that captures the essential issues and can be applied to a wide range of practical problems. Its explorations of recent developments in the field emphasize the relationship of new procedures to classical control theory, with a focus on single input and output systems that keeps concepts accessible to students with limited backgrounds. The text is geared toward a single-semester senior course or a graduate-level class for students of electrical engineering. The opening chapters constitute a basic treatment of feedback design. Topics include a detailed formulation of the control design program, the fundamental issue of performance/stability robustness tradeoff, and the graphical design technique of loopshaping. Subsequent chapters extend the discussion of the loopshaping technique and connect it with notions of optimality. Concluding chapters examine controller design via optimization, offering a mathematical approach that is useful for multivariable systems. |
| singular perturbation methods in control analysis and design: Boundary Control of PDEs Miroslav Krstic, Andrey Smyshlyaev, 2008-01-01 The text's broad coverage includes parabolic PDEs; hyperbolic PDEs of first and second order; fluid, thermal, and structural systems; delay systems; PDEs with third and fourth derivatives in space (including variants of linearized Ginzburg-Landau, Schrodinger, Kuramoto-Sivashinsky, KdV, beam, and Navier-Stokes equations); real-valued as well as complex-valued PDEs; stabilization as well as motion planning and trajectory tracking for PDEs; and elements of adaptive control for PDEs and control of nonlinear PDEs. |
| singular perturbation methods in control analysis and design: Introduction to Control Engineering Ajit K. Mandal, 2006 The Text Is Written From The Engineer'S Point Of View To Explain The Basic Oncepts Involved In Feedback Control Theory. The Material In The Text Has Been Organized For Gradual And Sequential Development Of Control Theory Starting With A Statement Of The Task Of A Control Engineer At The Very Outset. The Book Is Tended For An Introductory Undergraduate Course In Control Systems For Engineering Students.This Text Presents A Comprehensive Analysis And Design Of Continuous-Time Control Systems And Includes More Than Introductory Material For Discrete Systems With Adequate Guidelines To Extend The Results Derived In Connection Continuous-Time Systems. The Prerequisite For The Reader Is Some Elementary Owledge Of Differential Equations, Vector-Matrix Analysis And Mechanics. Transfer Function And State Variable Models Of Typical Components And Subsystems Have Been Derived In The Appendix At The End Of The Book.Most Of The Materials Including Solved And Unsolved Problems Presented In The Book Have Been Class-Tested In Senior Undergraduates And First Year Graduate El Courses In The Field Of Control Systems At The Electronics And Telecommunication Engineering Department, Jadavpur University. Matlab Is The Most Widely Used Cad Software Package In Universities Throughout The World. Some Representative Matlab Scripts Used For Solving Problems Are Cluded At The End Of Each Chapter. The Detailed Design Steps Of Fuzzy Logic Based Controller Using Simulink And Matlab Has Been Provided In The Book To Give The Student A Head Start In This Emerging Discipline.A Chapter Has Been Included To Deal With Nonlinear Components And Their Analysis G Matlab And Simulink Through User Defined S-Functions. Finally, A Chapter Has Been Included To Deal With The Implementation Of Digital Controllers On Finite Bit Computer, To Bring Out The Problems Associated With Digital Trollers. In View Of Extensive Use Of Matlab For Rapid Verification Of Controller Designs, Some Notes For Using Matlab Script M-Files And Function M-Files Are Included At The End Of The Book. |
| singular perturbation methods in control analysis and design: Data Analysis for Direct Numerical Simulations of Turbulent Combustion Heinz Pitsch, Antonio Attili, 2020-05-28 This book presents methodologies for analysing large data sets produced by the direct numerical simulation (DNS) of turbulence and combustion. It describes the development of models that can be used to analyse large eddy simulations, and highlights both the most common techniques and newly emerging ones. The chapters, written by internationally respected experts, invite readers to consider DNS of turbulence and combustion from a formal, data-driven standpoint, rather than one led by experience and intuition. This perspective allows readers to recognise the shortcomings of existing models, with the ultimate goal of quantifying and reducing model-based uncertainty. In addition, recent advances in machine learning and statistical inferences offer new insights on the interpretation of DNS data. The book will especially benefit graduate-level students and researchers in mechanical and aerospace engineering, e.g. those with an interest in general fluid mechanics, applied mathematics, and the environmental and atmospheric sciences. |
| singular perturbation methods in control analysis and design: Feedback Systems Karl Johan Åström, Richard Murray, 2021-02-02 The essential introduction to the principles and applications of feedback systems—now fully revised and expanded This textbook covers the mathematics needed to model, analyze, and design feedback systems. Now more user-friendly than ever, this revised and expanded edition of Feedback Systems is a one-volume resource for students and researchers in mathematics and engineering. It has applications across a range of disciplines that utilize feedback in physical, biological, information, and economic systems. Karl Åström and Richard Murray use techniques from physics, computer science, and operations research to introduce control-oriented modeling. They begin with state space tools for analysis and design, including stability of solutions, Lyapunov functions, reachability, state feedback observability, and estimators. The matrix exponential plays a central role in the analysis of linear control systems, allowing a concise development of many of the key concepts for this class of models. Åström and Murray then develop and explain tools in the frequency domain, including transfer functions, Nyquist analysis, PID control, frequency domain design, and robustness. Features a new chapter on design principles and tools, illustrating the types of problems that can be solved using feedback Includes a new chapter on fundamental limits and new material on the Routh-Hurwitz criterion and root locus plots Provides exercises at the end of every chapter Comes with an electronic solutions manual An ideal textbook for undergraduate and graduate students Indispensable for researchers seeking a self-contained resource on control theory |
| singular perturbation methods in control analysis and design: Robust Control Design with MATLAB® Da-Wei Gu, Petko H. Petkov, Mihail M Konstantinov, 2006-03-30 Shows readers how to exploit the capabilities of the MATLAB® Robust Control and Control Systems Toolboxes to the fullest using practical robust control examples. |
| singular perturbation methods in control analysis and design: Geometric Control Theory Velimir Jurdjevic, 1997 Geometric control theory is concerned with the evolution of systems subject to physical laws but having some degree of freedom through which motion is to be controlled. This book describes the mathematical theory inspired by the irreversible nature of time evolving events. The first part of the book deals with the issue of being able to steer the system from any point of departure to any desired destination. The second part deals with optimal control, the question of finding the best possible course. An overlap with mathematical physics is demonstrated by the Maximum principle, a fundamental principle of optimality arising from geometric control, which is applied to time-evolving systems governed by physics as well as to man-made systems governed by controls. Applications are drawn from geometry, mechanics, and control of dynamical systems. The geometric language in which the results are expressed allows clear visual interpretations and makes the book accessible to physicists and engineers as well as to mathematicians. |
| singular perturbation methods in control analysis and design: Perturbation Methods in Applied Mathematics J. Kevorkian, J.D. Cole, 2013-03-09 This book is a revised and updated version, including a substantial portion of new material, of J. D. Cole's text Perturbation Methods in Applied Mathe matics, Ginn-Blaisdell, 1968. We present the material at a level which assumes some familiarity with the basics of ordinary and partial differential equations. Some of the more advanced ideas are reviewed as needed; therefore this book can serve as a text in either an advanced undergraduate course or a graduate level course on the subject. The applied mathematician, attempting to understand or solve a physical problem, very often uses a perturbation procedure. In doing this, he usually draws on a backlog of experience gained from the solution of similar examples rather than on some general theory of perturbations. The aim of this book is to survey these perturbation methods, especially in connection with differ ential equations, in order to illustrate certain general features common to many examples. The basic ideas, however, are also applicable to integral equations, integrodifferential equations, and even to_difference equations. In essence, a perturbation procedure consists of constructing the solution for a problem involving a small parameter B, either in the differential equation or the boundary conditions or both, when the solution for the limiting case B = 0 is known. The main mathematical tool used is asymptotic expansion with respect to a suitable asymptotic sequence of functions of B. |
| singular perturbation methods in control analysis and design: Mathematical Control Theory Eduardo D. Sontag, 2013-11-21 Mathematics is playing an ever more important role in the physical and biologi cal sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and rein force the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and to encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mathematics Sci ences (AMS) series, which will focus on advanced textbooks and research-level monographs. v Preface to the Second Edition The most significant differences between this edition and the first are as follows: • Additional chapters and sections have been written, dealing with: nonlinear controllability via Lie-algebraic methods, variational and numerical approaches to nonlinear control, including a brief introduction to the Calculus of Variations and the Minimum Principle, - time-optimal control of linear systems, feedback linearization (single-input case), nonlinear optimal feedback, controllability of recurrent nets, and controllability of linear systems with bounded controls. |
| singular perturbation methods in control analysis and design: Spectral Methods Jie Shen, Tao Tang, Li-Lian Wang, 2011-08-25 Along with finite differences and finite elements, spectral methods are one of the three main methodologies for solving partial differential equations on computers. This book provides a detailed presentation of basic spectral algorithms, as well as a systematical presentation of basic convergence theory and error analysis for spectral methods. Readers of this book will be exposed to a unified framework for designing and analyzing spectral algorithms for a variety of problems, including in particular high-order differential equations and problems in unbounded domains. The book contains a large number of figures which are designed to illustrate various concepts stressed in the book. A set of basic matlab codes has been made available online to help the readers to develop their own spectral codes for their specific applications. |
| singular perturbation methods in control analysis and design: Optimal Control Theory with Aerospace Applications Joseph Z. Ben-Asher, 2010 Optimal control theory is a mathematical optimization method with important applications in the aerospace industry. This graduate-level textbook is based on the author's two decades of teaching at Tel-Aviv University and the Technion Israel Institute of Technology, and builds upon the pioneering methodologies developed by H.J. Kelley. Unlike other books on the subject, the text places optimal control theory within a historical perspective. Following the historical introduction are five chapters dealing with theory and five dealing with primarily aerospace applications. The theoretical section follows the calculus of variations approach, while also covering topics such as gradient methods, adjoint analysis, hodograph perspectives, and singular control. Important examples such as Zermelo's navigation problem are addressed throughout the theoretical chapters of the book. The applications section contains case studies in areas such as atmospheric flight, rocket performance, and missile guidance. The cases chosen are those that demonstrate some new computational aspects, are historically important, or are connected to the legacy of H.J. Kelley.To keep the mathematical level at that of graduate students in engineering, rigorous proofs of many important results are not given, while the interested reader is referred to more mathematical sources. Problem sets are also included. |
| singular perturbation methods in control analysis and design: Optimal Control Systems D. Subbaram Naidu, 2018-10-03 The theory of optimal control systems has grown and flourished since the 1960's. Many texts, written on varying levels of sophistication, have been published on the subject. Yet even those purportedly designed for beginners in the field are often riddled with complex theorems, and many treatments fail to include topics that are essential to a thorough grounding in the various aspects of and approaches to optimal control. Optimal Control Systems provides a comprehensive but accessible treatment of the subject with just the right degree of mathematical rigor to be complete but practical. It provides a solid bridge between traditional optimization using the calculus of variations and what is called modern optimal control. It also treats both continuous-time and discrete-time optimal control systems, giving students a firm grasp on both methods. Among this book's most outstanding features is a summary table that accompanies each topic or problem and includes a statement of the problem with a step-by-step solution. Students will also gain valuable experience in using industry-standard MATLAB and SIMULINK software, including the Control System and Symbolic Math Toolboxes. Diverse applications across fields from power engineering to medicine make a foundation in optimal control systems an essential part of an engineer's background. This clear, streamlined presentation is ideal for a graduate level course on control systems and as a quick reference for working engineers. |
| singular perturbation methods in control analysis and design: Linear Controller Design Stephen P. Boyd, Craig H. Barratt, 1991 |
| singular perturbation methods in control analysis and design: Applied Nonlinear Control Jean-Jacques E. Slotine, Weiping Li, 1991 In this work, the authors present a global perspective on the methods available for analysis and design of non-linear control systems and detail specific applications. They provide a tutorial exposition of the major non-linear systems analysis techniques followed by a discussion of available non-linear design methods. |
| singular perturbation methods in control analysis and design: Power System Dynamics and Stability Peter W. Sauer, M. A. Pai, 1998 For a one-semester senior or beginning graduate level course in power system dynamics. This text begins with the fundamental laws for basic devices and systems in a mathematical modeling context. It includes systematic derivations of standard synchronous machine models with their fundamental controls. These individual models are interconnected for system analysis and simulation. Singular perturbation is used to derive and explain reduced-order models. |
| singular perturbation methods in control analysis and design: Uncertain Models and Robust Control Alexander Weinmann, 2012-12-06 Control systems particularly designed to manage uncertainties are called robust control system. Choosing appropriate design methods, the influence of uncertainties on the closed-loop behaviour can be reduced to a large extent. Most of the important areas of robust control are covered. The aim of the book is to provide an introduction to the theory and methods of robust control system design, to present a coherent body of knowledge, to clarify and unify presentation of significant derivations and proofs. The book contains a thorough treatment of important material of uncertainties and robust control which is scattered throughout the literature. |
| singular perturbation methods in control analysis and design: Switching in Systems and Control Daniel Liberzon, 2012-12-06 l\lany systems encountered in practice involve a coupling between contin uous dynamics and discrete events. Systems in which these two kinds of dynamics coexist and interact are usually called hybrid. For example, the following phenomena give rise to hybrid behavior: a valve or a power switch opening and closing; a thermostat turning the heat on and off; biological cells growing and dividing; a server switching between buffers in a queueing network; aircraft entering, crossing, and leaving an air traffic control region; dynamics of a car changing abruptly due to wheels locking and unlocking on ice. Hybrid systems constitute a relatively new and very active area of current research. They present interesting theoretical challenges and are important in many real-world problems. Due to its inherently interdisci plinary nature, the field has attracted the attention of people with diverse backgrounds, primarily computer scientists, applied mathematicians, and engineers. Researchers with a background and interest in continuous-time systems and control theory are concerned primarily with properties of the contin uous dynamics, such as Lyapunov stability. A detailed investigation of the discrete behavior, on the other hand, is usually not a goal in itself. In fact, rather than dealing with specifics of the discrete dynamics, it is often use ful to describe and analyze a more general category of systems which is known to contain a particular model of interest. |
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