Robust Nonlinear Control Design

, by Freeman, Randy A.; Kokotovic, Petar V.

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ISBN: 9780817647582 | 0817647589
Cover: Paperback
Copyright: 1/1/2008

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This softcover book summarizes Lyapunov design techniques for nonlinear systems and raises important issues concerning large-signal robustness and performance. The authors have been the first to address some of these issues, and they report their findings in this text. The researcher who wishes to enter the field of robust nonlinear control could use this book as a source of new research topics. For those already active in the field, the book may serve as a reference to a recent body of significant work. Finally, the design engineer faced with a nonlinear control problem will benefit from the techniques presented here.

Introduction	p. 1
A Lyapunov framework for robust control	p. 3
Inverse optimality in robust stabilization	p. 6
Recursive Lyapunov design	p. 9
Set-Valued Maps	p. 15
Continuity of set-valued maps	p. 17
Upper and lower semicontinuity	p. 17
Lipschitz and Hausdorff continuity	p. 19
Marginal functions	p. 21
Intersections	p. 23
Continuity of intersections	p. 23
Lipschitz continuity of intersections	p. 24
Selection theorems	p. 28
Michael's theorem	p. 28
Minimal selections	p. 28
Lipschitz selections	p. 29
Parameterized maps	p. 30
Summary	p. 32
Robust Control Lyapunov Functions	p. 33
Nonlinear robust stabilization	p. 35
System description	p. 35
Problem statement	p. 39
Nonlinear disturbance attenuation	p. 40
Input-to-state stability	p. 41
Nonlinear small gain theorems	p. 42
Disturbance attenuation vs. robust stabilization	p. 43
Robust control Lyapunov functions	p. 45
Control Lyapunov functions	p. 46
Rclf: general definition	p. 48
Rclf: state-feedback for time-invariant systems	p. 49
Rclf: absence of disturbance input	p. 51
Rclf implies robust stabilizability	p. 53
Small control property	p. 56
Output feedback	p. 58
Locally Lipschitz state feedback	p. 60
Robust stabilizability implies rclf	p. 61
Summary	p. 63
Inverse Optimality	p. 65
Optimal stabilization: obstacles and benefits	p. 66
Inverse optimality, sensitivity reduction, and stability margins	p. 67
An introductory example	p. 69
Pointwise min-norm control laws	p. 71
General formula	p. 72
Jointly affine systems	p. 75
Feedback linearizable systems	p. 76
Inverse optimal robust stabilization	p. 78
A preliminary result	p. 78
A differential game formulation	p. 79
Main theorem	p. 81
Proof of the main theorem	p. 83
Terminology and technical lemmas	p. 83
Construction of the function r	p. 85
Proof of the key proposition	p. 88
Proof of optimality	p. 91
Extension to finite horizon games	p. 93
A finite horizon differential game	p. 94
Main theorem: finite horizon	p. 95
Proof of the main theorem	p. 96
Summary	p. 100
Robust Backstepping	p. 101
Lyapunov redesign	p. 103
Matched uncertainty	p. 103
Beyond the matching condition	p. 105
Recursive Lyapunov design	p. 107
Class of systems: strict feedback form	p. 108
Construction of an rclf	p. 110
Backstepping design procedure	p. 115
A benchmark example	p. 117
Flattened rclf's for softer control laws	p. 119
Hardening of control laws	p. 119
Flattened rclf's	p. 123
Design example: elimination of chattering	p. 126
Nonsmooth backstepping	p. 127
Clarke's generalized directional derivative	p. 130
Nonsmooth rclf's	p. 131
Backstepping with nonsmooth nonlinearities	p. 132
Summary	p. 136
Measurement Disturbances	p. 137
Effects of measurement disturbances	p. 138
Loss of global stability	p. 138
Loss of global stabilizability	p. 139
Design for strict feedback systems	p. 143
Measurement constraint for ISS	p. 143
Backstepping with measurement disturbances	p. 145
Initialization step	p. 148
Recursion step	p. 150
Design procedure and example	p. 157
Summary	p. 160
Dynamic Partial State Feedback	p. 161
Nonlinear observer paradigm	p. 162
Extended strict feedback systems	p. 162
Assumptions and system structure	p. 163
Controller design	p. 167
Main result	p. 167
Controller design for n = 1	p. 168
Conceptual controllers and derivatives	p. 172
Backstepping lemma	p. 174
Controller design for n [greater than or equal] 2	p. 177
Proof of the main result	p. 179
Design example	p. 180
Truth model and design model	p. 182
Full state feedback design	p. 186
Partial state feedback design	p. 194
Summary	p. 201
Robust Nonlinear PI Control	p. 203
Problem formulation	p. 204
Class of systems	p. 204
Design objective	p. 206
Controller design	p. 208
Main result	p. 208
Technical lemma	p. 209
Controller design for r = 1	p. 211
Backstepping construction	p. 215
Controller design for r [greater than or equal] 2	p. 218
Proof of the main result	p. 222
Design example	p. 223
Summary	p. 227
Local K-continuity in metric spaces	p. 229
K-continuity	p. 230
Local K-continuity	p. 233
CK-continuity	p. 237
Bibliography	p. 241
Index	p. 255
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Robust Nonlinear Control Design

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