NONLINEAR AND ADAPTIVE CONTROL DESIGN
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NONLINEAR AND ADAPTIVE CONTROL DESIGN Miroslav Krstic loannis Kanellakopoulos Petar Kokotovic A WILEY-INTERSCIENCE PUBLICATION JOHN WILEY & SONS, INC. New York / Chichester / Brisbane / Toronto / Singapore
Transcript of NONLINEAR AND ADAPTIVE CONTROL DESIGN
NONLINEAR AND ADAPTIVE CONTROL DESIGN
Miroslav Krstic loannis Kanellakopoulos Petar Kokotovic
A WILEY-INTERSCIENCE PUBLICATION
JOHN WILEY & SONS, INC.
New York / Chichester / Brisbane / Toronto / Singapore
Contents
i i i 2 3 4 5 7 7 9
10 11 11 12 14 15 15 16 17
1.4 Notation 17 Notes and References 17
1 State Feedback 19
2 Design Tools for Stabilization 21 2.1 Stability 22
2.1.1 Main stability theorems 22 2.1.2 Control Lyapunov functions (elf) 25
2.2 Backstepping 29 2.2.1 Integrator backstepping 29 2.2.2 Example: active Suspension (parallel) 37 2.2.3 Feedback linearization and zero dynamics 39
Introduction 1.1
1.2
1.3
Adaptive Linear Control 1.1.1 Emergence of adaptive control 1.1.2 Achievements of adaptive linear control 1.1.3 Adaptive control as dynamic nonlinear feedback 1.1.4 Lyapunov-based design 1.1.5 Estimation-based design Adaptive Nonlinear Control 1.2.1 A nonlinear challenge 1.2.2 A structural obstacle 1.2.3 Early results Preview of the Main Topics 1.3.1 Classes of nonlinear Systems 1.3.2 Adaptive backstepping and tuning functions 1.3.3 Modular designs 1.3.4 Output-feedback designs 1.3.5 Linear Systems 1.3.6 Transient Performance 1.3.7 Caveat: robustness
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X CONTENTS
2.2.4 Stabilization of cascade Systems 42 2.2.5 Block backstepping with zero dynamics 49 2.2.6 Example: active Suspension (series) 55
2.3 Recursive Design Procedures 58 2.3.1 Strict-feedback Systems 58 2.3.2 Pure-feedback Systems 61 2.3.3 Block-strict-feedback Systems 64
2.4 Design Flexibility: Jet Engine Example 66 2.4.1 Jet engine stall and surge 67 2.4.2 A two-step design 68 2.4.3 Avoiding cancellations 70
2.5 Stabilization with Uncertainty 72 2.5.1 Nonlinear damping 73 2.5.2 Backstepping with uncertainty 80 2.5.3 Robust strict-feedback Systems 84
Notes and References 86
Adaptive Backstepping Design 87 3.1 Adaptation as Dynamic Feedback 88 3.2 Adaptive Backstepping 92
3.2.1 Adaptive integrator backstepping 92 3.2.2 Adaptive block backstepping 98
3.3 Recursive Design Procedures 99 3.3.1 Parametric strict-feedback Systems 99 3.3.2 Multi-input Systems 103 3.3.3 Parametric block-strict-feedback Systems 105
3.4 Extended Matching Design 110 3.4.1 Reducing the overparametrization 110 3.4.2 Example: biochemical process 113 3.4.3 TVansient Performance improvement 115
Notes and References 121
Tuning Functions Design 123 4.1 Adaptive Control Lyapunov Functions • 124
4.1.1 Departure from certainty equivalence 124 4.1.2 Certainty equivalence for a modified System 128 4.1.3 Adaptive backstepping via aclf 134
4.2 Set-Point Regulation 139 4.2.1 Design procedure 140 4.2.2 Stability and convergence 151 4.2.3 Passivity 154
4.3 Tracking 1 5 6
4.3.1 Design procedure 157 4.3.2 Trajectory initialization 162
CONTENTS XI
4.4 Transient Performance 165 4.4.1 £ 2 Performance 165 4.4.2 £;» Performance 166
4.5 Extensions 168 4.5.1 Unknown Virtual control coefficients 168 4.5.2 Block-strict-feedback Systems 173 4.5.3 Pu're-feedback Systems 175
4.6 Example: Aircraft Wing Rock 180 Notes and References 183
5 Modular Design with Passive Identifiers 185 5.1 Weakness of Certainty Equivalence 186 5.2 ISS-Control Lyapunov Functions 189 5.3 ISS-Controller Design 198 5.4 Observers for Strict Passivity 206 5.5 z-Passive Scheme 209 5.6 x-Passive Scheme 212 5.7 Transient Performance 218 5.8 SG-Scheme (Weak Modularity) 222
5.8.1 Controller design 223 5.8.2 Scheme with strengthened identifier 225
5.9 Unknown Virtual Control Coefficients 229 5.9.1 Controller design 229 5.9.2 Passive adaptive scheme 232
Notes and References 233
6 Modular Design with Swapping Identifiers 235 6.1 ISS-Controller 235 6.2 Swapping and Static Parametric Models 237 6.3 z-Swapping Scheme 239 6.4 z-Swapping Scheme 248 6.5 Transient Performance 254
6.5.1 Simulation examples 259 6.6 SG-Scheme 265 6.7 Schemes with Weak ISS-Controller 271 6.8 Unknown Virtual Control Coefficients 277 Notes and References 282
II Output Feedback 283
7 Output-Feedback Design Tools 285 7.1 Observer Backstepping 285
7.1.1 Unmeasured states
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7.1.2 Output-feedback Systems 291 7.2 MIMO Design: Induction Motor 294 7.3 Adaptive Observer Backstepping 301
7.3.1 An introductory example 301 7.3.2 Parametric output-feedback Systems 307 7.3.3 Example: single-link flexible robot 313
7.4 Extensions 315 7.4.1 Interlaced controller-observer design 315 7.4.2 Design with partial-state feedback 320
Notes and References 324
Tuning Functions Designs 327 8.1 Design with K-Filters 329
8.1.1 Filters and observer 329 8.1.2 Adaptive Controller design 332 8.1.3 Stability 340 8.1.4 Transient Performance 346
8.2 Design with MT-Filters 348 8.2.1 Filtered transformations and observer 348 8.2.2 Adaptive Controller design 351 8.2.3 Stability 357 8.2.4 Transient Performance 363
8.3 Example: Levitated Ball 365 Notes and References 369
Modular Designs 371 9.1 ISS-Controller Design 372 9.2 y-Passive Scheme 380 9.3 «/-Swapping Scheme 384 9.4 z-Swapping Scheme 388 9.5 Schemes with Parametric z-Model 392 9.6 Transient Performance 394
9.6.1 Passive schemes 394 9.6.2 Swapping schemes 397
9.7 Swapping Schemes with Weak ISS-Controller 400 9.8 Schemes with MT-Filters 403
9.8.1 ISS-observer 404 9.8.2 ISS-controller 405 9.8.3 x-Passive scheme 407 9.8.4 e-Swapping scheme 409 9.8.5 Transient Performance 412
Notes and References 416
CONTENTS Xlll
10 Linear Systems 417 10.1 State Estimation Filters 418 10.2 Tuning Functions Design 422
10.2.1 Design procedure 422 10.2.2 Stability analysis 434 10.2.3 Passivity 438 10.2.4 Design example 440
10.3 Properties of the Nonadaptive System 443 10.3.1 Underlying linear Controller 443 10.3.2 Parametric robustness and nonadaptive Performance 448
10.4 Transient Performance with Tuning Functions 453 10.4.1 Transient Performance of the adaptive System 454 10.4.2 Performance improvement due to adaptation 459
10.5 Comparison with a Traditional Scheme 464 10.5.1 Choice of a traditional scheme 464 10.5.2 Comparison of the schemes 465
10.6 Modular Designs 470 10.6.1 SG-controller 470 10.6.2 y-Passive scheme 473 10.6.3 x-Swapping scheme 477 10.6.4 Comparison: modular vs. tuning functions design 482
10.7 Summary 484 Notes and References 484
Appendices 487
A Lyapunov Stability and Convergence 489
B Input-Output Stability 493
C Input-to-State Stability 501
D Passivity 507
E Parameter Projection 511
F NonKnear Swapping 515
G Differential Geometrie Conditions 521 G.l Partial-State-Feedback Forms 521 G.2 Output-Feedback Forms 533 G.3 Full-State-Feedback Forms 535
Bibliography 541
Index 559
