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《Dynamic Surface Control of Uncertain Nonlinear Systems》.pdf
Cover
Communications and Control Engineering
Dynamic Surface Control of Uncertain Nonlinear Systems
ISBN 9780857296313
Preface
Contents
Abbreviations
Part I: Theory
Chapter 1: Introduction
1.1 A Brief History of Dynamic Surface Control
1.2 Sliding Mode Control
1.3 Integrator Backstepping
1.3.1 Mismatched Uncertainties
1.3.2 Design Methodology
1.4 Multiple Sliding Surface Control
1.5 Dynamic Surface Control
1.5.1 Motivating Example
1.5.2 An LMI Approach
1.6 Book Organization
1.7 Origin of the Book
Chapter 2: Dynamic Surface Control
2.1 Motivation
2.2 Problem Statement
2.3 Design Procedure
2.4 Augmented Error Dynamics
2.5 Quadratic Stabilization
2.5.1 Nominal Error Dynamics
2.5.2 Norm-Bounded Error Dynamics
2.5.3 Diagonal Norm-Bounded Error Dynamics
2.6 Ultimate and Quadratic Boundedness
Chapter 3: Robustness to Uncertain Nonlinear Systems
3.1 Uncertain Lipschitz Systems
3.1.1 Problem Statement
3.1.2 Quadratic Stability and Tracking
3.2 DSC with Nonlinear Damping
3.2.1 Problem Statement
3.2.2 Stabilization and Quadratic Boundedness
3.3 Input-Output Stability
Chapter 4: Observer-Based Dynamic Surface Control
4.1 Nonlinear Observer Design
4.1.1 Problem Statement
4.1.2 Quadratic Stability of Observer
4.1.3 Design of Observer Gain Matrix
Step 1. Calculation of Stability Margin
Step 2. Coordinate Transformation
Step 3. Design of Observer Gain Matrix L
4.2 A Separation Principle
4.2.1 Preliminary Design of ODSC
4.2.2 Augmented Error Dynamics
4.2.3 Separation Principle of Error Dynamics
4.3 Quadratic Stabilization and Tracking
4.4 Consideration of Uncertainty
4.4.1 Redesign of Nonlinear Observer
4.4.2 Design Procedure of ODSC
Chapter 5: Constrained Stabilization
5.1 Problem Statement and Preliminaries
5.2 Local Regulation and Regions of Attraction
5.3 Robust Constrained Stabilization
Chapter 6: Multi-Input Multi-Output Mechanical Systems
6.1 Fully-Actuated Mechanical System
6.2 Synthesis of Dynamic Surface Control
6.2.1 Error Dynamics
6.2.2 Synthesis for Stabilization
6.2.2.1 Stability Analysis
6.2.2.2 Decomposition of Controller Gains
6.2.2.3 Optimal Design of DSC
6.2.3 Synthesis for Quadratic Tracking
6.2.4 Avoiding Cancelations
6.3 Extension to Rigid Body Dynamics
6.4 Decentralized Dynamic Surface Control
6.4.1 Preliminary Design of DDSC
6.4.2 Augmented Error Dynamics
6.4.3 Decentralized Stabilization
Augmented Error Dynamics
Design of Controller Gains
Part II: Applications
Chapter 7: Automated Vehicle Control
7.1 Application to Longitudinal Vehicle Control
7.1.1 Engine and Brake Control via DSC
7.1.2 Switched Closed Loop Error Dynamics
7.1.3 Simultaneous Quadratic Boundedness
7.1.4 Input-Output Stability
7.2 Passive Fault Tolerant Control
7.2.1 Problem Statement
7.2.2 Error Dynamics for a Faulty Nonlinear System
7.2.3 Fault Classification
7.2.3.1 Fault Detection and Diagnosis
7.2.3.2 Fault Classification for Switched System
Chapter 8: Fault Tolerant Control for AHS
8.1 Controller Reconfiguration
8.1.1 Observer-Based DSC
8.1.2 Trajectory Reconfiguration
8.2 Longitudinal Control for an Automated Transit Bus
8.2.1 Longitudinal Control via DSC
8.2.2 Quadratic Tracking and Validation
8.3 Active Fault Tolerant Control
8.3.1 Error Dynamics for Faulty System
8.3.2 Sensor Fault Handling
Observer Design
Sensor Fault Handling
8.3.3 Trajectory Reconfiguration for Longitudinal Control
Case I: Tolerable Parametric Fault
Case II: Trajectory Reconfiguration
Chapter 9: Biped Robot Control
9.1 Hybrid Biped Model
9.2 Trajectory Generation
9.3 Motion Control for SSP and DSP
9.3.1 Application of Dynamic Surface Control
9.3.2 Augmented Error Dynamics
9.3.3 Piecewise Quadratic Boundedness
9.4 Simulation Results
Appendix Proofs
A.1 Proof of Lemma 2.1
Lemma 2.1
A.2 Proof of Lemma 3.1
Lemma 3.1
A.3 Proof of Lemma 3.2
Lemma 3.2
A.4 Proof of Theorem 5.3
Theorem 5.3
References
Index
Communications and Control Engineering
For other titles published in this series, go to
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Stability and Stabilization of Infinite Dimensional
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Control of Linear Systems with Regulation and Input
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Control of Complex and Uncertain Systems
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Subspace Methods for System Identification
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Polynomial and Rational Matrices
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Simulation-based Algorithms for Markov Decision
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Iterative Learning Control
Hyo-Sung Ahn, Kevin L. Moore and YangQuan Chen
Distributed Consensus in Multi-vehicle Cooperative
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Control of Singular Systems with Random Abrupt
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Constructions of Strict Lyapunov Functions
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Wei Ren and Yongcan Cao
Bongsob Song r J. Karl Hedrick
Dynamic Surface
Control of Uncertain
Nonlinear Systems
An LMI Approach
Bongsob Song
Department of Mechanical Engineering
Ajou University
San 5, Wonchon-dong, Yeongtong-gu
443-749 Suwon
Korea, Republic of (South Korea)
bsong@ajou.ac.kr
J. Karl Hedrick
Department of Mechanical Engineering
University of California at Berkeley
5104 Etcheverry Hall
Mailstop 1740
94720 Berkeley
USA
khedrick@me.berkeley.edu
ISSN 0178-5354
ISBN 978-0-85729-631-3
DOI 10.1007/978-0-85729-632-0
Springer London Dordrecht Heidelberg New York
e-ISBN 978-0-85729-632-0
British Library Cataloguing in Publication Data
A catalogue record for this book is available from the British Library
Library of Congress Control Number: 2011929130
© Springer-Verlag London Limited 2011
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Preface
This monograph provides a detailed practical and theoretical introduction to non-
linear control system design for the use of engineers and scientists. It will present
systematic design methods, such as those that have been developed for linear sys-
tems, to address nonlinear problems. Linear control theory has a limited ability to
tackle highly nonlinear systems. Our purpose here is to extend the recent develop-
ments in convex optimization of linear systems to nonlinear systems. A new non-
linear control algorithm known as “dynamic surface control (DSC)” using convex
optimization is presented. It provides an effective design methodology for design-
ing robust controllers for uncertain nonlinear systems. Sample applications will be
provided to demonstrate how DSC can be effectively used to solve design problems
in both the automotive and robotic fields.
This book is primarily intended for graduate students in nonlinear control theory,
but can also serve as a source of applications for researchers in control design in the
area of mechatronic systems such as automotive and robotic control. A wide variety
of problems ranging from the design of DSC to extensions to output feedback, input
saturation, multi-input multi-output, and fault tolerant control are considered. The
results are shown to apply to a class of nonlinear and interconnected systems, in
particular to automated vehicle control and biped robot control.
This book is divided in two parts. The first part addresses theoretical results for
nonlinear control system design. In Chap. 2 a new method of analyzing the sta-
bility of a class of nonlinear systems by using the DSC design approach is pre-
sented. Based on quadratic stability theory, feasibility of the fixed controller gains
for quadratic stabilization and tracking can be tested by solving a convex optimiza-
tion problem. This approach is extended to problems with consideration of the fol-
lowing constraints, as we advance from chapter to chapter:
• a class of uncertainties: Chap. 3
• output feedback: Chap. 4
• input saturation: Chap. 5
• multi-input multi-output: Chap. 6.
v
vi
Preface
The second part of the book introduces applications of theoretical results to vehi-
cle and robot control. The relation between chapters and the results of the first part
of the book is summarized as follows:
• Fault classification for vehicle control in Chap. 7: extension of the results in
Chaps. 2 and 3 to switched nonlinear systems
• Fault tolerant control for an automated vehicle in Chap. 8: extension of the results
in Chap. 4 to switched nonlinear systems
• Biped robot control in Chap. 9: application of the results in Chaps. 2 and 6 to
interconnected mechanical systems.
The authors are particularly indebted to former graduate students in the Vehicle
Dynamics and Control Lab at UC Berkeley: J. Green and M. Won contributed to
the idea of multiple sliding surface control; S. Choi and D. McMahon conducted
engine and vehicle control using multiple sliding surface control; D. Swaroop and
C. Gerdes triggered the use of dynamic surface control for uncertain nonlinear sys-
tems and applied the idea to vehicle control; P. Yip extended the result to adaptive
dynamic surface control; S. Raghavan and R. Rajamani provided a systematic pro-
cedure for nonlinear observer design. There are probably more names we should
acknowledge for their contributions in a long line of simulations and applications.
We would like to thank each one of them.
We also want to acknowledge the collaboration with California PATH at UC
Berkeley. Especially more than 15 researchers including the first author developed
the automated transit bus and demonstrated its feasibility in 2003, and some of re-
sults and pictures are included in this book. The implementation of the longitudi-
nal control described in this book would not have succeeded without A. Howell,
S. Dickey, and many other researchers at the California PATH research program.
The first author wishes to thank his former students at the Automatic Control
Lab at Ajou University; J. Choi worked on simulations of the biped robot control.
He also wants to thank his family for their endless support: his wife Moonjeung
and sons Ryan and Kyle. Furthermore, he is grateful to Ajou University and UC
Berkeley for providing an environment to write this monograph at Berkeley.
The second author would like to thank his wife Carlyle and daughters Ashley,
Tristan and Ryan for their interest and support over the years. He would also like to
thank his many, many students, who have taught him so much.
Suwon, Korea
Berkeley, California, USA
Bongsob Song
J. Karl Hedrick
Contents
Part I
Theory
1
2
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Introduction .
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1.1 A Brief History of Dynamic Surface Control
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1.2 Sliding Mode Control
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1.3 Integrator Backstepping .
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1.3.1 Mismatched Uncertainties . . . . . . . . . . . . . . . . . .
1.3.2 Design Methodology . . . . . . . . . . . . . . . . . . . .
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1.5.1 Motivating Example . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . .
1.5.2 An LMI Approach . . .
1.6 Book Organization . . . . . . . . . . . . . . . . . . . . . . . . . .
1.7 Origin of the Book . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4 Multiple Sliding Surface Control
1.5 Dynamic Surface Control
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Dynamic Surface Control
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2.2 Problem Statement .
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2.3 Design Procedure . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 Augmented Error Dynamics . .
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2.5 Quadratic Stabilization .
2.5.1 Nominal Error Dynamics
. . . . . . . . . . . . . . . . . .
2.5.2 Norm-Bounded Error Dynamics . . . . . . . . . . . . . . .
2.5.3 Diagonal Norm-Bounded Error Dynamics
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2.6 Ultimate and Quadratic Boundedness . . . . . . . . . . . . . . . .
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Robustness to Uncertain Nonlinear Systems . . . . . . . . . . . . . .
3.1 Uncertain Lipschitz Systems . .
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3.1.1 Problem Statement . . . . . . . . . . . . . . . . . . . . . .
3.1.2 Quadratic Stability and Tracking . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . .
3.2.1 Problem Statement . . . . . . . . . . . . . . . . . . . . . .
3.2 DSC with Nonlinear Damping .
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vii
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