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E-raamat: Stabilization and Regulation of Nonlinear Systems: A Robust and Adaptive Approach

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Stabilization and Regulation of Nonlinear Systems: A Robust and Adaptive ApproachSuurem pilt
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The core of this textbook is a systematic and self-contained treatment of the nonlinear stabilization and output regulation problems. Its coverage embraces both fundamental concepts and advanced research outcomes and includes many numerical and practical examples. Several classes of important uncertain nonlinear systems are discussed. The state-of-the art solution presented uses robust and adaptive control design ideas in an integrated approach which demonstrates connections between global stabilization and global output regulation allowing both to be treated as stabilization problems.

Stabilization and Regulation of Nonlinear Systems takes advantage of rich new results to give students up-to-date instruction in the central design problems of nonlinear control, problems which are a driving force behind the furtherance of modern control theory and its application. The diversity of systems in which stabilization and output regulation become significant concerns in the mathematical formulation of practical control solutions—whether in disturbance rejection in flying vehicles or synchronization of Lorenz systems with harmonic systems—makes the text relevant to readers from a wide variety of backgrounds. Many exercises are provided to facilitate study and solutions are freely available to instructors via a download from springerextras.com.

Striking a balance between rigorous mathematical treatment and engineering practicality, Stabilization and Regulation of Nonlinear Systems is an ideal text for graduate students from many engineering and applied-mathematical disciplines seeking a contemporary course in nonlinear control. Practitioners and academic theorists will also find this book a useful reference on recent thinking in this field.

Arvustused

The book focuses on two design problems for nonlinear continuous-time control systems, namely stabilization and output regulation. The book is useful for both researchers and for use in graduate courses in control engineering. (Tibor Takács, Mathematical Reviews, August, 2015) 

1 Introduction
1(14)
1.1 Nonlinear Systems
1(3)
1.2 Examples of Nonlinear Control Systems
4(5)
1.3 Organization of the Book
9(2)
1.4 Notes and References
11(1)
1.5 Problems
12(3)
References
13(2)
2 Fundamentals of Nonlinear Systems
15(52)
2.1 Stability Concepts
15(4)
2.2 Robust Stability
19(3)
2.3 Tools for Adaptive Control
22(8)
2.4 Input-to-State Stability
30(6)
2.5 Changing Supply Function
36(9)
2.6 Universal Adaptive Control
45(6)
2.7 Small Gain Theorem
51(7)
2.8 Notes and References
58(1)
2.9 Problems
58(9)
References
64(3)
3 Classification of Nonlinear Control Systems
67(24)
3.1 Normal Form and Zero Dynamics
67(10)
3.2 Typical Nonlinear Control Systems
77(6)
3.3 Examples of Nonlinear Control Systems
83(5)
3.3.1 The Duffing Equation
83(1)
3.3.2 The Lorenz System
83(2)
3.3.3 Chua's Circuit
85(2)
3.3.4 The FitzHugh-Nagumo Model
87(1)
3.4 Notes and References
88(1)
3.5 Problems
88(3)
References
89(2)
4 Robust Stabilization
91(36)
4.1 An Overview of the Approach
91(3)
4.2 Output Feedback Systems
94(7)
4.3 Lower Triangular Systems
101(8)
4.4 Reduction of Control Gain
109(6)
4.5 Robust Stabilization of Chua's Circuit
115(5)
4.6 Notes and References
120(2)
4.7 Problems
122(5)
References
124(3)
5 Adaptive Stabilization
127(30)
5.1 A Motivating Example
127(3)
5.2 Adaptive Stabilization: Tuning Functions Design
130(7)
5.3 Robust Adaptive Stabilization
137(14)
5.3.1 Systems with Relative Degree One
138(3)
5.3.2 Systems with High Relative Degree
141(10)
5.4 Adaptive Stabilization of the Duffing Equation
151(3)
5.5 Notes and References
154(1)
5.6 Problems
155(2)
References
156(1)
6 Universal Adaptive Stabilization
157(40)
6.1 Output Feedback Systems
157(6)
6.2 Lower Triangular Systems
163(14)
6.2.1 Parameterized Changing Supply Function
164(4)
6.2.2 A Recursive Procedure
168(4)
6.2.3 Controller Synthesis
172(5)
6.3 Unknown Control Direction
177(11)
6.4 Adaptive Stabilization of the Hyperchaotic Lorenz System
188(5)
6.5 Notes and References
193(1)
6.6 Problems
194(3)
References
195(2)
7 Robust Output Regulation: A Framework
197(42)
7.1 Problem Description
198(6)
7.2 Steady-State Generator
204(11)
7.2.1 Linear Immersion Assumption
206(4)
7.2.2 Nonlinear Immersion Assumption
210(2)
7.2.3 Generalized Linear Immersion Assumption
212(3)
7.3 Internal Model
215(5)
7.4 From Output Regulation to Stabilization
220(4)
7.5 Linear Robust Output Regulation
224(9)
7.6 Notes and References
233(1)
7.7 Problems
233(6)
References
236(3)
8 Global Robust Output Regulation
239(48)
8.1 Systems with Relative Degree One
239(10)
8.2 Output Feedback Systems
249(10)
8.3 Lower Triangular Systems
259(10)
8.4 Nonlinear Exosystems
269(5)
8.5 Uncertainties with Unknown Boundary
274(3)
8.5.1 Systems with Relative Degree One
274(1)
8.5.2 Output Feedback Systems
275(1)
8.5.3 Lower Triangular Systems
276(1)
8.6 Asymptotic Tracking of the Lorenz System
277(5)
8.7 Notes and References
282(1)
8.8 Problems
283(4)
References
285(2)
9 Output Regulation with Uncertain Exosystems
287(26)
9.1 Systems with Relative Degree One
287(8)
9.2 Systems with High Relative Degree
295(5)
9.3 Disturbance Rejection of Lower Triangular Systems
300(7)
9.4 Disturbance Rejection of the FitzHugh--Nagumo Model
307(4)
9.5 Notes and References
311(1)
9.6 Problems
311(2)
References
312(1)
10 Attitude Control of a Rigid Spacecraft
313(26)
10.1 Quaternion Based Rigid Spacecraft Model
313(3)
10.2 Problem Formulation
316(5)
10.3 A Special Case for Motivation
321(2)
10.4 Disturbance with Known Frequencies
323(7)
10.5 Disturbance with Unknown Frequencies
330(6)
10.6 Notes and References
336(3)
References
337(2)
11 Appendix
339(16)
11.1 Some Theorems on Nonlinear Systems
339(1)
11.2 Technical Lemmas
340(4)
11.3 Proof of Theorem 2.12
344(8)
11.4 Notes and References
352(3)
References
353(2)
Index 355
Zhiyong Chen studied Automatic Control at the University of Science and Technology of China from 1995 to 2000 and was awarded the B. Eng degree in 2000. He was awarded the M.Phil and Ph.D. degrees from the Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong both in the area of systems and control and in 2002 and 2005, respectively. He was a Research Associate with the University of Virginia from 2005 to 2006 and is currently a Senior Lecture with the University of Newcastle, Australia. His research area is mainly nonlinear control theory and applications. He received the China State Natural Science Award, Class II, in 2010, the best paper award of the Eighth International Conference on Control, Automation, Robotics and Vision in 2004, the best paper awards of the Eighth and the Tenth World Congress on Intelligent Control and Automation in 2010 and 2012. He is/was associate editor of IEEE Transactions on Automatic Control, Systems and Control Letters and several other journals.

Jie Huang studied Power Engineering at Fuzhou University from 1977 to 1979 and Circuits and Systems at Nanjing University of Science and Technology (NUST) from 1979 to 1982. He got his Master's degree from NUST in 1982 and was a faculty member there from 1982 to 1986. He completed his Ph.D. study in automatic control at the Johns Hopkins University in 1990 and subsequently held a post-doctoral fellowship there until July 1991. From August 1991 to July 1995,

he worked in industry in the USA. In September 1995, he joined the Department of Mechanical and Automation Engineering at the Chinese University of Hong Kong and is now a professor and chairman there. He served as a Science Advisor to the Leisure and Cultural Services Department of Hong Kong Special Administrative Region, and Honorary Advisor to Hong Kong Science Museum. His research interests include control theory and applications, robotics and automation, systems biology and guidance andcontrol of flight vehicles. He has authored two books and numerous papers. He received the China State Natural Science Award, Class II, in 2010, the Croucher Senior Research Fellowship award in 2006, and the best paper award of the Eighth International Conference on Control, Automation, Robotics and Vision in 2004. He is a CAA Fellow, IFAC Fellow and IEEE Fellow.

Jie Huang is/was editor, associate editor or guest editor of several journals. He was Distinguished Lecturer of the IEEE Control Systems Society from 2005 to 2008 and a member of the Board of Governors of IEEE Control Systems Society from 2006 to 2007. He has delivered plenary/keynote speeches in numerous international conferences.
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