应用非线性控制（英文版） (2010 年度畅销榜NO.9530 )

本书详细探讨了现代非线性系统的分析与设计技术，并提供了分析非线性系统的工具。主要内容包括相平面分析、描述函数分析、反馈线性化、滑动控制以及自适应控制等。另外，还提供了大量例题与习题，便于教学。
本书结构安排合理，实践性强，适合作为高等院校理工科专业的教材，同时对非线性控制初学者以及相关工程技术人员来说也是一本很好的参考书。

Preface iii
1. Introduction
1.1 Why Nonlinear Control ? 1
1.2 Nonlinear System Behavior 4
1.3 An Overview of the Book 12
1.4 Notes and References 13
Part I: Nonlinear Systems Analysis 14
Introduction to Part I 14
2. Phase Plane Analysis 17
2.1 Concepts of Phase Plane Analysis 18
2.1.1 Phase Portraits 18
2.1.2 Singular Points 20
2.1.3 Symmetry in Phase Plane Portraits 22
2.2 Constructing Phase Portraits 23
2.3 Determining Time from Phase Portraits 29
2.4 Phase Plane Analysis of Linear Systems 30
2.5 Phase Plane Analysis of Nonlinear Systems 32
2.6 Existence of Limit Cycles 36
2.7 Summary 38
2.8 Notes and References 38
2.9 Exercises 38
3. Fundamentals of Lyapunov Theory 40
3.1 Nonlinear Systems and Equilibrium Points 41
3.2 Concepts of Stability 47
3.3 Linearization and Local Stability 53
3.4 Lyapunov's Direct Method 57
3.4.1 Positive Definite Functions and Lyapunov Functions 58
3.4.2 Equilibrium Point Theorems 61
3.4.3 lnvariant Set Theorems 68
3.5 System Analysis Based on Lyapunov's Direct Method 76
3.5.1 L yapunov Analysis of Linear Time-lnvariant Systems 77
3.5.2 Krasovskii' s Method 83
3.5.3 The Variable Gradient Method 86
3.5.4 Physically Motivated Lyapunov Functions 88
3.5.5 Performance Analysis 91
3.6 Control Design Based on Lyapunov's Direct Method 94
3.7 Summary 95
3.8 Notes and References 96
3.9 Exercises 97
4. Advanced Stability Theory 100
4.1 Concepts of Stability for Non-Autonomous Systems I01
4.2 Lyapunov Analysis of Non-Autonomous Systems 105
4.2.1 Lyapunov' s Direct Method for Non-Autonomous Systems 105
4.2.2 Lyapunov Analysis of Linear Time-Varying Systems 114
4.2.3 * The Linearization Method for Non-Autonomous Systems 116
4.3 * Instability Theorems 117
4.4 * Existence of Lyapunov Functions 120
4.5 Lyapunov-Like Analysis Using Barbalat's Lemma 122
4.5.1 Asymptotic Properties of Functions and Their Derivatives 122
4.5.2 Barbalat' s Lemma 123
4.6 Positive Linear Systems 126
4.6.1 PR and SPR Transfer Functions 126
4.6.2 The Kalman-Yakubovich Lemma 130
4.6.3 Positive Real Transfer Matrices 131
4.7 The Passivity Formalism 132
4.7.1 Block Combinations 132
4.7.2 Passivity in Linear Systems 137
4.8 * Absolute Stability 142
4.9 * Establishing Boundedness of Signals 147
4.10 * Existence and Unicity of Solutions 151
4.11 Summary 153
4.12 Notes and References 153
4.13 Exercises 154
5. Describing Function Analysis 157
5.1 Describing Function Fundamentals 158
5.1.1 An Example of Describing Function Analysis 158
5.1.2 Applications Domain 162
5.1.3 Basic Assumptions 164
5.1.4 Basic Definitions 165
5.1.5 Computing Describing Functions 167
5.2 Common Nonlinearities In Control Systems 169
5.3 Describing Functions of Common Nonlinearities 172
5.4 Describing Function Analysis of Nonlinear Systems 179
5.4.1 The Nyquist Criterion and Its Extension 180
5.4.2 Existence of Limit Cycles 182
5.4.3 Stability of Limit Cycles 184
5.4.4 Reliability of Describing Function Analysis 186
5.5 Summary 187
5.6 Notes and References 188
5.7 Exercises 188
Part II: Nonlinear Control Systems Design 191
Introduction to Part H 191
6. Feedback Linearization 207
6.1 Intuitive Concepts 208
6.1.1 Feedback Linearization And The Canonical Form 208
6.1.2 Input-State Linearization 213
6.1.3 Input-Output Linearization 216
6.2 Mathematical Tools 229
6.3 Input-State Linearization of SISO Systems 236
6.4 Input-Output Linearization of SISO Systems 246
6.5 * Multi-Input Systems 266
6.6 Summary 270
6.7 Notes and References 271
6.8 Exercises 271
7. Sliding Control 276
7.1 Sliding Surfaces 277
7.1.1 A Notational Simplification 278
7.1.2 * Filippov's Construction of the Equivalent Dynamics 283
7.1.3 Perfect Performance - At a Price 285
7.1.4 Direct Implementations of Switching Control Laws 289
7.2 Continuous Approximations of Switching Control Laws 290
7.3 The Modeling/Performance Trade-Offs 301
7.4 * Multi-Input Systems 303
7.5 Summary 306
7.6 Notes and References 307
7.7 Exercises 307
8. Adaptive Control 311
8.1 Basic Concepts in Adaptive Control 312
8.1.1 Why Adaptive Control ? 312
8.1.2 What Is Adaptive Control ? 315
8.1.3 How To Design Adaptive Controllers ? 323
8.2 Adaptive Control of First-Order Systems 326
8.3 Adaptive Control of Linear Systems With Full State Feedback 335
8.4 Adaptive Control of Linear Systems With Output Feedback 339
8.4.1 Linear Systems With Relative Degree One 340
8.4.2 Linear Systems With Higher Relative Degree 346
8.5 Adaptive Control of Nonlinear Systems 350
8.6 Robustness of Adaptive Control Systems 353
8.7 * On-Line Parameter Estimation 358
8.7.1 Linear Pararnetrization Model 359
8.7.2 Prediction-Error-Based Estimation Methods 364
8.7.3 The Gradient Estimator 364
8.7.4 The Standard Least-Squares Estimator 370
8.7.5 Least-Squares With Exponential Forgetting 374
8.7.6 Bounded-Gain Forgetting 376
8.7.7 Concluding Remarks and Implementation Issues 381
8.8 Composite Adaptation 382
8.9 Summary 388
8.10 Notes and References 389
8.11 Exercises 389
9. Control of Multi-Input Physical Systems 392
9.1 Robotics as a Prototype 393
9.1.1 Position Control 394
9.1.2 Trajectory Control 397
9.2 Adaptive Robot Trajectory Control 403
9.2.1 The Basic Algorithm 404
9.2.2 * Composite Adaptive Trajectory Control 411
9.3 Putting Physics in Control 416
9.3.1 High-Frequency Unmodeled Dynamics 416
9.3.2 Conservative and Dissipative Dynamics 418
9.3.3 Robotics as a Metaphor 419
9.4 Spacecraft Control 422
9.4.1 The Spacecraft Model 422
9.4.2 Attitude Control 425
9.5 Summary 432
9.6 Notes and References 433
9.7 Exercises 433
BIBLIOGRAPHY 437
INDEX 459

Jean-Jacques E. Slotine于麻省理工学院获得博士学位. 现任麻省理工学院机械工程系及信息科学系教授, 非线性系统实验室主任. 他的主要研究方向包括机器人学. 非线性控制. 学习系统等.

In recent years, the availability of powerful low-cost microprocessors has spurred great advances in the theory and applications of nonlinear control. In terms of theory, major strides have been made in the areas of feedback linearization, sliding control, and nonlinear adaptation techniques. In terms of applications, many practical nonlinear control systems have been developed, ranging from digital "fly-by-wire" flight control systems for aircraft, to "drive-by-wire" automobiles, to advanced robotic and space systems. As a result, the subject of nonlinear control is occupying an increasingly important place in automatic control engineering, and has become a necessary part of the fundamental background of control engineers. This book, based on a course developed at Mrr, is intended as a textbook for senior and graduate students, and as a self-study book for practicing engineers. Its objective is to present the fundamental results of modem nonlinear control while keeping the mathematical complexity to a minimum, and to demonstrate their use and implications in the design of practical nonlinear control systems. Although a major motivation of this book is to detail the many recent developments in nonlinear control, classical techniques such as phase plane analysis and the describing function method are also treated, because of their continued practical importance. In order to achieve our fundamental objective, we have tried to bring the following features to this book: ~ Readability: Particular attention is paid to the readability of the book by carefully organizing the concepts, intuitively interpreting the major results, and selectively using the mathematical tools. The readers are only assumed to have had one introductory control course. No mathematical background beyond ordinary differential equations and elementary matrix algebra is required. For each new result, interpretation is emphasized rather than mathematics. For each major result, we try to ask and answer the following key questions: What does the result intuitively and physically mean? How can it be applied to practical problems? What is its relationship to other theorems? All major concepts and results are demonstrated by examples. We believe that learning and generalization from examples are crucialfor proficiency in applying any theoretical result. ~ Practicality: The choice 'and emphasis of materials is guided by the basic objective of making an engineer or student capable of dealing with practical control problems in industry. Some results of mostly theoretical interest are not included. The selected materials, in one way or another, are intended to allow readers to gain insights into the solution of real problems. ~ Comprehensiveness: The book contains both classical materials, such as Lyapunov analysis and describing function techniques, and more modem topics such as feedback linearization, adaptive control, and sliding control. To facilitate digestion, asterisks are used to indicate sections which, given their relative complexity, can be safely skipped in a first reading. ~ Currentness: In the past few years, a number of major results have been obtained in nonlinear control, particularly in nonlinear control system design and in robotics. It is one of the objectives of this book to present these new and important developments, and their implications, in a clear, easily understandable fashion. The book can thus be used as a reference and a guide to the active literature in these fields. The book is divided into two major parts. Chapters 2-5 present the major analytical tools that can be used to study a nonlinear system, while chapters 6-9 treat the major nonlinear controller design techniques. Each chapter is supplied with exercises, allowing the reader to further explore specific aspects of the material discussed. A detailed index and a bibliography are provided at the end of the book. The material included exceeds what can be taught in one semester or selflearned in a short period. The book can be studied in many ways, according to the particular interests of the reader or the instructor. We recommend that a first reading include a detailed study of chapter 3 (basic Lyapunov theory), sections 4.5-4.7 (Barbalat's lemma and passivity tools), section 6.1 and parts of sections 6.2-6.4 (feedback linearization), chapter 7 (sliding control), sections 8.1-8.3 and 8.5 (adaptive control of linear and nonlinear systems), and chapter 9 (control of multi-input physical systems). Conversely, sections denoted with an asterisk can be skipped in a first reading. Many colleagues, students, and friends greatly contributed to this book through stimulating discussions and judicious suggestions. Karl Hedrick provided us with continued enthusiasm and encouragement, and with many valuable comments and suggestions. Discussions with Karl AstriSm and Semyon Meerkov helped us better define the tone of the book and its mathematical level. Harry Asada, Jo Bentsman, Marika DiBenedetto, Olay Egeland, Neville Hogan, Marija Ilic, Lars Nielsen, Ken Salisbury, Sajhendra Singh, Mark Spong, David Wormley, and Dana Yoerger provided many useful suggestions and much moral support. Barbara Hove created most of the nicer drawings in the book; Giinter Niemeyer's expertise and energy was invaluable in setting up the computing and word processing environments; Hyun Yang greatly helped with the computer simulations; all three provided us with extensive technical and editorial comments. The book also greatly benefited from the interest and enthusiasm of many students who took the course at MIT. Partial summer support for the first author towards the development of the book was provided by Gordon Funds. Finally, the energy and professionalism of Tim Bozik and Jennifer Wenzel at Prentice-Hall were very effective and highly appreciated. Jean-Jacques E. SIotine Weiping Li