L1 Adaptive Control Theory: Guaranteed Robustness with Fast Adaptation (Advances in Design and Control)

338 Pages·2010·10.17 MB·English

by  Naira Hovakimyan

L
Adaptive

1
Control Theory
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Advances in Design and Control
SIAM’s Advances in Design and Control series consists of texts and monographs dealing with all areas of
design and control and their applications. Topics of interest include shape optimization, multidisciplinary
design, trajectory optimization, feedback, and optimal control. The series focuses on the mathematical and
computational aspects of engineering design and control that are usable in a wide variety of scientific and
engineering disciplines.
Editor-in-Chief
Ralph C. Smith, North Carolina State University
Editorial Board
Athanasios C. Antoulas, Rice University
Siva Banda, Air Force Research Laboratory
Belinda A. Batten, Oregon State University
John Betts, The Boeing Company (retired)
Stephen L. Campbell, North Carolina State University
Michel C. Delfour, University of Montreal
Max D. Gunzburger, Florida State University
J. William Helton, University of California, San Diego
Arthur J. Krener, University of California, Davis
Kirsten Morris, University of Waterloo
Richard Murray, California Institute of Technology
Ekkehard Sachs, University of Trier
Series Volumes
Hovakimyan, Naira, and Cao, Chengyu, L Adaptive Control Theory: Guaranteed Robustness with Fast Adaptation
1
Speyer, Jason L., and Jacobson, David H., Primer on Optimal Control Theory
Betts, John T., Practical Methods for Optimal Control and Estimation Using Nonlinear Programming, Second
Edition
Shima, Tal and Rasmussen, Steven, eds., UAV Cooperative Decision and Control: Challenges and Practical
Approaches
Speyer, Jason L. and Chung, Walter H., Stochastic Processes, Estimation, and Control
Krstic, Miroslav and Smyshlyaev, Andrey, Boundary Control of PDEs: A Course on Backstepping Designs
Ito, Kazufumi and Kunisch, Karl, Lagrange Multiplier Approach to Variational Problems and Applications
Xue, Dingyü, Chen, YangQuan, and Atherton, Derek P., Linear Feedback Control: Analysis and Design
with MATLAB
Hanson, Floyd B., Applied Stochastic Processes and Control for Jump-Diffusions: Modeling, Analysis, and
Computation
Michiels, Wim and Niculescu, Silviu-Iulian, Stability and Stabilization of Time-Delay Systems: An Eigenvalue-
Based Approach
Ioannou, Petros and Fidan, Barıs, Adaptive Control Tutorial
Bhaya, Amit and Kaszkurewicz, ¸Eugenius, Control Perspectives on Numerical Algorithms and Matrix Problems
Robinett III, Rush D., Wilson, David G., Eisler, G. Richard, and Hurtado, John E., Applied Dynamic Programming
for Optimization of Dynamical Systems
Huang, J., Nonlinear Output Regulation: Theory and Applications
Haslinger, J. and Mäkinen, R. A. E., Introduction to Shape Optimization: Theory, Approximation, and Computation
Antoulas, Athanasios C., Approximation of Large-Scale Dynamical Systems
Gunzburger, Max D., Perspectives in Flow Control and Optimization
Delfour, M. C. and Zolésio, J.-P., Shapes and Geometries: Analysis, Differential Calculus, and Optimization
Betts, John T., Practical Methods for Optimal Control Using Nonlinear Programming
El Ghaoui, Laurent and Niculescu, Silviu-Iulian, eds., Advances in Linear Matrix Inequality Methods in Control
Helton, J. William and James, Matthew R., Extending H Control to Nonlinear Systems: Control of Nonlinear
1
Systems to Achieve Performance Objectives
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L
Adaptive

1
Control Theory
Guaranteed Robustness
with Fast Adaptation
Naira Hovakimyan
University of Illinois
Urbana, Illinois
Chengyu Cao
University of Connecticut
Storrs, Connecticut
Society for Industrial and Applied Mathematics
Philadelphia
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Copyright © 2010 by the Society for Industrial and Applied Mathematics.
10 9 8 7 6 5 4 3 2 1
All rights reserved. Printed in the United States of America. No part of this book may
be reproduced, stored, or transmitted in any manner without the written permission
of the publisher. For information, write to the Society for Industrial and Applied
Mathematics, 3600 Market Street, 6th Floor, Philadelphia, PA 19104-2688 USA.
Trademarked names may be used in this book without the inclusion of a trademark
symbol. These names are used in an editorial context only; no infringement of trademark
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Advanced Digital Logic is a registered trademark of Advanced Digital Logic Inc.
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MATLAB and Simulink are registered trademarks of The MathWorks, Inc. For
MATLAB product information, please contact The MathWorks, Inc., 3 Apple Hill Drive,
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Figure 1 in the preface appears courtesy of the United States Army.
Figure 2 in the preface appears courtesy of the Naval Postgraduate School.
Figures 3 & 4 in the preface appear courtesy of NASA.
Figure 6.1 used with permission from NASA.
Library of Congress Cataloging-in-Publication Data

Hovakimyan, Naira.
L adaptive control theory : guaranteed robustness with fast adaptation / Naira
1
Hovakimyan, Chengyu Cao.
p. cm. -- (Advances in design and control ; 21)
Includes bibliographical references and index.
ISBN 978-0-898717-04-4
1. Adaptive control systems. 2. Robust control. I. Cao, Chengyu. II. Title.
TJ217.H68 2010
629.8’36--dc22
2010013646
is a registered trademark.
DC21_Hovakimyan-Cao-FM.indd 4 7/15/2010 8:24:15 AM
To my parents Emma and Viktor, and to my sister Anna with love and gratitude
NH
To my wife Xingwei and our son Lucas Bochao, as well as to our parents
Jinrong, Guangju, Runkuan, and Yageng with love and gratitude
CC
y
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Contents
Foreword xi
Preface xiii
1 Introduction 1
1.1 HistoricalOverview . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 TwoDifferentArchitecturesofAdaptiveControl . . . . . . . . . . . . 4
1.2.1 DirectMRAC . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.2 DirectMRACwithStatePredictor . . . . . . . . . . . . 6
1.2.3 TuningChallenges . . . . . . . . . . . . . . . . . . . . . 7
1.3 SavingtheTime-DelayMargin . . . . . . . . . . . . . . . . . . . . . 8
1.4 UniformlyBoundedControlSignal . . . . . . . . . . . . . . . . . . . 12
2 StateFeedbackinthePresenceofMatchedUncertainties 17
2.1 SystemswithUnknownConstantParameters . . . . . . . . . . . . . . 17
2.1.1 ProblemFormulation . . . . . . . . . . . . . . . . . . . 18
2.1.2 L AdaptiveControlArchitecture . . . . . . . . . . . . . 18
1
2.1.3 AnalysisoftheL AdaptiveController:Scaling . . . . . 19
1
2.1.4 Design of the L Adaptive Controller: Robustness and
1
Performance . . . . . . . . . . . . . . . . . . . . . . . . 25
2.1.5 SimulationExample . . . . . . . . . . . . . . . . . . . . 29
2.1.6 LoopShapingviaState-PredictorDesign . . . . . . . . . 31
2.2 SystemswithUncertainSystemInputGain . . . . . . . . . . . . . . . 35
2.2.1 ProblemFormulation . . . . . . . . . . . . . . . . . . . 36
2.2.2 L AdaptiveControlArchitecture . . . . . . . . . . . . . 37
1
2.2.3 PerformanceBoundsoftheL AdaptiveController . . . 39
1
2.2.4 PerformanceinthePresenceofNonzeroTrajectory
InitializationError . . . . . . . . . . . . . . . . . . . . . 44
2.2.5 Time-DelayMarginAnalysis . . . . . . . . . . . . . . . 47
2.2.6 Gain-MarginAnalysis . . . . . . . . . . . . . . . . . . . 59
2.2.7 SimulationExample:RoboticArm . . . . . . . . . . . . 59
2.3 ExtensiontoSystemswithUnmodeledActuatorDynamics . . . . . . 67
2.3.1 ProblemFormulation . . . . . . . . . . . . . . . . . . . 67
2.3.2 L AdaptiveControlArchitecture . . . . . . . . . . . . . 68
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2.3.3 AnalysisoftheL AdaptiveController . . . . . . . . . . 70
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viii Contents
2.3.4 SimulationExample:Rohrs’Example . . . . . . . . . . . 76
2.4 L AdaptiveControllerforNonlinearSystems . . . . . . . . . . . . . 80
1
2.4.1 ProblemFormulation . . . . . . . . . . . . . . . . . . . 80
2.4.2 L AdaptiveControlArchitecture . . . . . . . . . . . . . 81
1
2.4.3 AnalysisoftheL AdaptiveController . . . . . . . . . . 83
1
2.4.4 SimulationExample:WingRock . . . . . . . . . . . . . 90
2.5 L AdaptiveControllerinthePresenceofNonlinearUnmodeled
1
Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
2.5.1 ProblemFormulation . . . . . . . . . . . . . . . . . . . 94
2.5.2 L AdaptiveControlArchitecture . . . . . . . . . . . . . 95
1
2.5.3 AnalysisoftheL AdaptiveController . . . . . . . . . . 97
1
2.5.4 SimulationExample . . . . . . . . . . . . . . . . . . . . 105
2.6 FilterDesignforPerformanceandRobustnessTrade-Off . . . . . . . 111
2.6.1 OverviewofStochasticOptimizationAlgorithms . . . . . 113
2.6.2 LMI-BasedFilterDesign . . . . . . . . . . . . . . . . . 114
3 StateFeedbackinthePresenceofUnmatchedUncertainties 121
3.1 L AdaptiveControllerforNonlinearStrict-FeedbackSystems . . . . 121
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3.1.1 ProblemFormulation . . . . . . . . . . . . . . . . . . . 121
3.1.2 L AdaptiveControlArchitecture . . . . . . . . . . . . . 122
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3.1.3 AnalysisoftheL AdaptiveController . . . . . . . . . . 125
1
3.1.4 SimulationExample . . . . . . . . . . . . . . . . . . . . 136
3.2 L AdaptiveControllerinthePresenceofUnmatchedUncertainties . 140
1
3.2.1 ProblemFormulation . . . . . . . . . . . . . . . . . . . 141
3.2.2 L AdaptiveControlArchitecture . . . . . . . . . . . . . 142
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3.2.3 AnalysisoftheL AdaptiveController . . . . . . . . . . 145
1
3.2.4 SimulationExample . . . . . . . . . . . . . . . . . . . . 154
3.3 Piecewise-ConstantAdaptiveLawsforSystemswithUnmatched
Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
3.3.1 ProblemFormulation . . . . . . . . . . . . . . . . . . . 159
3.3.2 L AdaptiveControlArchitecture . . . . . . . . . . . . . 160
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3.3.3 AnalysisoftheL AdaptiveController . . . . . . . . . . 164
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3.3.4 SimulationExample . . . . . . . . . . . . . . . . . . . . 172
4 OutputFeedback 179
4.1 L Adaptive Output Feedback Controller for First-Order Reference
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Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
4.1.1 ProblemFormulation . . . . . . . . . . . . . . . . . . . 180
4.1.2 L AdaptiveControlArchitecture . . . . . . . . . . . . . 180
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4.1.3 AnalysisoftheL AdaptiveOutputFeedbackController 183
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4.1.4 DesignfortheL -NormCondition . . . . . . . . . . . . 189
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4.1.5 SimulationExample . . . . . . . . . . . . . . . . . . . . 190
4.2 L AdaptiveOutputFeedbackControllerforNon-SPRReference
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Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
4.2.1 ProblemFormulation . . . . . . . . . . . . . . . . . . . 192
4.2.2 L AdaptiveControlArchitecture . . . . . . . . . . . . . 193
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4.2.3 AnalysisoftheL AdaptiveController . . . . . . . . . . 198
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4.2.4 SimulationExample:Two-CartBenchmarkProblem . . . 207
5 L AdaptiveControllerforTime-VaryingReferenceSystems 211
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5.1 L AdaptiveControllerforLinearTime-VaryingSystems . . . . . . . 211
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5.1.1 ProblemFormulation . . . . . . . . . . . . . . . . . . . 211
5.1.2 L AdaptiveControlArchitecture . . . . . . . . . . . . . 212
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5.1.3 AnalysisofL AdaptiveController . . . . . . . . . . . . 214
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5.1.4 SimulationExample . . . . . . . . . . . . . . . . . . . . 218
5.2 L AdaptiveControllerforNonlinearSystemswithUnmodeled
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Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
5.2.1 ProblemFormulation . . . . . . . . . . . . . . . . . . . 223
5.2.2 L AdaptiveControlArchitecture . . . . . . . . . . . . . 224
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5.2.3 AnalysisoftheL AdaptiveController . . . . . . . . . . 226
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5.2.4 SimulationExample . . . . . . . . . . . . . . . . . . . . 234
6 Applications,Conclusions,andOpenProblems 241
6.1 L AdaptiveControlinFlight . . . . . . . . . . . . . . . . . . . . . . 241
1
6.1.1 FlightValidationofL AdaptiveControlatNaval
1
PostgraduateSchool . . . . . . . . . . . . . . . . . . . . 243
6.1.2 L Adaptive Control Design for the NASA AirSTAR
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FlightTestVehicle . . . . . . . . . . . . . . . . . . . . . 254
6.1.3 OtherApplications . . . . . . . . . . . . . . . . . . . . . 259
6.2 KeyFeatures,Extensions,andOpenProblems . . . . . . . . . . . . . 260
6.2.1 MainFeaturesoftheL AdaptiveControlTheory . . . . 260
1
6.2.2 ExtensionsNotCoveredintheBook . . . . . . . . . . . 260
6.2.3 OpenProblems . . . . . . . . . . . . . . . . . . . . . . . 261
A SystemsTheory 263
A.1 VectorandMatrixNorms . . . . . . . . . . . . . . . . . . . . . . . . 263
A.1.1 VectorNorms . . . . . . . . . . . . . . . . . . . . . . . 263
A.1.2 InducedNormsofMatrices . . . . . . . . . . . . . . . . 264
A.2 SymmetricandPositiveDefiniteMatrices . . . . . . . . . . . . . . . 265
A.3 L-spacesandL-norms . . . . . . . . . . . . . . . . . . . . . . . . . 265
A.4 ImpulseResponseofLinearTime-InvariantSystems . . . . . . . . . . 267
A.5 ImpulseResponseofLinearTime-VaryingSystems . . . . . . . . . . 268
A.6 LyapunovStability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269
A.6.1 AutonomousSystems . . . . . . . . . . . . . . . . . . . 269
A.6.2 Time-VaryingSystems . . . . . . . . . . . . . . . . . . . 270
A.7 L-Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272
A.7.1 BIBOStabilityofLTISystems . . . . . . . . . . . . . . 273
A.7.2 BIBOStabilityforLTVSystems . . . . . . . . . . . . . 276
A.8 LinearParametrizationofNonlinearSystems . . . . . . . . . . . . . . 278
A.9 LinearTime-VaryingRepresentationofSystemswithLinear
UnmodeledDynamics . . . . . . . . . . . . . . . . . . . . . . . . . . 281
A.10 LinearTime-VaryingRepresentationofSystemswithLinear
UnmodeledActuatorDynamics . . . . . . . . . . . . . . . . . . . . . 283
A.11 PropertiesofControllableSystems . . . . . . . . . . . . . . . . . . . 285
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