Control of uncertain systems–modelling, approximation, and design: a workshop on the occasion of Keith Glover’s 60th birthday

Bruce A. Francis, Malcolm C. Smith, Jan C. Willems3540317546, 9783540317548

This Festschrift contains a collection of articles by friends, co-authors, colleagues, and former Ph.D. students of Keith Glover, Professor of Engineering at the University of Cambridge, on the occasion of his sixtieth birthday. Professor Glover’s scientific work spans a wide variety of topics, the main themes being system identification, model reduction and approximation, robust controller synthesis, and control of aircraft and engines. The articles in this volume are a tribute to Professor Glover’s seminal work in these areas.

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Table of contents :
front-matter.pdf……Page 1
0329toc.pdf……Page 0
To Keith Glover on the occasion of his sixtieth birthday……Page 5
CV — Keith Glover……Page 6
Research students supervised……Page 7
Articles in scienti.c journals and edited books……Page 8
Selected conference papers……Page 13
Contents……Page 14
1 Introduction……Page 16
1.1 Systems of Interest……Page 17
1.2 Robust Stability Results for LPV Systems……Page 20
1.3 Contribution of This Paper……Page 21
2 LPV Framework……Page 22
2.1 Plant and Controller Fractional Descriptions……Page 23
2.2 Internal Stability and Multi-a.ne Parameter Dependence……Page 24
3 Controller Synthesis……Page 25
3.1 Parameter-Dependent Controller Construction……Page 26
3.2 Incorporating a Degree of Stability in the Frozen Parameter Design……Page 29
3.3 Securing a Quadratic Lyapunov Function with Multi-a.ne Parameter Dependence……Page 30
4 Design Procedure……Page 32
5 Numerical Example……Page 34
References……Page 37
1 Introduction……Page 39
2 Modeling of Supercavitating Vehicles……Page 41
2.1 Two Degree of Freedom Model with Delay……Page 42
3.1 Feedback Linearization……Page 46
3.2 Controllability Analysis of the Bimodal System……Page 48
4 Multivariable Pole Placement……Page 51
5 Control of a Supercavitating Vehicle Model……Page 53
6 Summary and Future Research……Page 56
References……Page 57
1 Introduction……Page 59
2 Moore-Penrose and Cramer-Rao……Page 60
3 Moore-Penrose and Smoothing……Page 62
4 Stable Systems; Partial Fraction Coordinates……Page 63
5 A Two Variable Identi.ability Gramian……Page 70
6 2D Transforms and the Resonant Case……Page 75
7 A Matrix Inequality……Page 76
8 Beyond NMR Spectroscopy……Page 77
References……Page 79
Notation……Page 80
2 Finite-Dimensional Systems……Page 81
2.1 Exponential Stability, Stabilisability and Detectability……Page 82
2.2 Coprime Factors and Graph Symbols……Page 83
3 The Gap Metric……Page 85
4 A Characterisation of the Gap for Approximation……Page 87
5 Concluding Remarks……Page 88
A Technical Lemma……Page 89
References……Page 90
1 Introduction……Page 92
2 Controllers with Internal Loop……Page 93
3 Formulation of the Problem……Page 98
4 The Suboptimal Nehari Problem……Page 99
5 Normalized Coprime Factorizations……Page 102
6 Robustly Stabilizing Controllers for State Linear Systems……Page 103
7 Integrated Nodes and Reciprocals……Page 106
References……Page 110
1 Introduction……Page 112
2 Preliminaries……Page 113
3 NLPV Systems……Page 114
4 Model Reduction of Strongly 2 -Stable NLPV Systems……Page 118
4.1 Balanced Truncation……Page 119
4.2 Error Bounds……Page 121
4.3 Eventually Periodic LPV Systems……Page 129
References……Page 130
1 Introduction……Page 132
2 Fixed Visibility Graph……Page 134
3 Limited Visibility Cameras……Page 136
4 Related Work……Page 144
5 Conclusions……Page 148
References……Page 149
1 Introduction……Page 151
2 Prediction Error Identi.cation Aspects……Page 155
3 Control Design Objectives and Control Design Method……Page 159
4 Demands on the Identi.cation Experiment……Page 160
5 The Cost of a Closed-Loop Identi.cation Experiment……Page 161
6 Identi.cation Experiments Without External Excitation……Page 162
7.1 Shortest Identi.cation Experiment for Control with Fixed F r ( . )……Page 163
7.2 Least costly identi.cation experiment with .xed data length……Page 165
7.3 Dealing with the Unknown Quantities θ θ and 0 N σ , e……Page 168
8 Simulation Results……Page 169
References……Page 172
1 Objectives of Automotive Control……Page 175
2.1 Model Classes……Page 177
2.2 Some Important Examples……Page 178
3.1 Introduction……Page 180
3.2 Some Important Examples……Page 182
3.3 Future Trends and Open Problems……Page 183
4.1 Introduction……Page 184
4.2 Description of PAC Car II……Page 185
4.3 Optimal Control Problem……Page 186
4.4 Optimization of the Driving Strategy……Page 187
References……Page 193
1 Introduction……Page 195
2.1 Control Law Development History……Page 196
2.2 Open Questions……Page 197
3.1 Method……Page 199
3.2 Application……Page 200
3.3 Results……Page 201
3.4 Using Pilot Commands……Page 202
4.1 Measuring Stability……Page 205
4.2 Review of FCL005 Stability……Page 206
4.3 Open Questions on Stability Requirements……Page 207
5.1 FCL005 Feedback Architecture……Page 208
5.2 Impact of Inner Loop on Uncertainty……Page 209
5.3 Non-diagonal Weights……Page 210
6.1 Implementation of FCL005……Page 211
6.2 Implementation in SISO Form……Page 212
7 Conclusions……Page 213
References……Page 214
1 Introduction……Page 215
2.1 Stages of Mitosis……Page 216
3.1 Actin……Page 218
3.2 Myosin-I……Page 219
3.4 Rho-Superfamily Members……Page 220
4 Mechanical Nature of the Cell……Page 221
4.1 Viscoelastic Properties of Cross-Linked Actin Networks……Page 223
4.3 The Yoneda-Dan Model of Cytokinesis……Page 224
4.4 Stages in Cytokinesis: Di.erent Phases……Page 226
6 Role of Mechanical Feedback……Page 227
6.1 Evidence for Mechanical Feedback in Cytokinesis……Page 228
6.2 Evaluating Models of Mechanical Feedback……Page 229
7 Conclusions……Page 230
References……Page 231
1 Introduction……Page 237
2 Master Equation for Chemical Reactions……Page 238
3 Toggle Switch……Page 242
4 CME for Toggle Switch……Page 243
5 Truncation and Reduction to Standard Form……Page 245
6 Irreducibility……Page 247
7 Simulation Results……Page 249
8 Conclusion……Page 252
References……Page 253
1 Introduction……Page 255
2 Dynamic Programming Background……Page 256
3 Computing Decentralized Policies……Page 258
4 The Linear Programming Approach……Page 260
5 Example……Page 263
References……Page 267
1 Introduction……Page 269
2.1 The Optimization Problem……Page 271
2.2 Loop Shaping Design Procedure……Page 272
3 Motorcycle Model……Page 273
4.1 Standard Characteristics……Page 274
4.2 Characteristics of Machines Compensated by Mechanical Networks……Page 277
5.1 Controller Design……Page 280
5.2 Controller Performance……Page 282
6 Conclusions……Page 283
References……Page 285
1 A Personal Introduction……Page 288
2 Data in the Frequency Domain……Page 289
3 Periodic Inputs……Page 290
4 Transients and Initial States……Page 291
5 Continuous-Time Data with Band-Limited Input……Page 294
6 Other Intersample Behaviors……Page 295
7.1 Input-Output Fourier Transform Data……Page 297
7.3 Estimation and Validation……Page 298
7.4 Some Further Features……Page 299
8 Conclusions……Page 300
References……Page 301
1 Introduction……Page 303
2 Problem Formulation and Preliminaries……Page 304
3 -Suboptimal Filters via Finite Dimensional Relaxation……Page 309
4.1 Fixed Order Filter Design……Page 311
4.2 Casting the Finite-Dimensional Problem (Equation 4) as an SDP……Page 312
4.3 Bounds via Worst Case Analysis……Page 313
5 Suboptimal Filters……Page 314
6 Example……Page 315
7 Conclusion……Page 317
8.1 Proof of Lemma 1……Page 318
8.3 Problem Setup and Preliminaries……Page 319
8.4 Filtering Result……Page 320
8.5 Worst-Case Analysis……Page 321
8.6 Branch and Bound Algorithm……Page 322
References……Page 323
1 Introduction……Page 326
1.1 Notation……Page 329
2.2 De.nitions……Page 330
2.3 Robust Stability……Page 332
2.4 Generalized Plants Considered……Page 334
2.5 Robust Performance……Page 337
3.1 De.ne the Robust Stability Margin b ( P, C )……Page 343
3.2 When Is the Given Data Consistent and What Are All Solutions?……Page 344
3.3 De.ne the Solution Set …….Page 345
3.5 Write the Winding Number Condition Independent of Δ……Page 346
3.6 State Robust Stability and Robust Performance Theorems……Page 348
4 Other Structures……Page 351
References……Page 352
1.1 Stochastic Modelling……Page 354
1.2 Algorithms for Finding Genes……Page 357
2.1 Formula for Estimating the Transition Matrix of a Markov Chain……Page 358
2.2 Bernstein’s Inequality for I.I.D. and Alpha-Mixing Samples……Page 360
2.3 Accuracy and Con.dence Estimates for Markov Chains……Page 362
3.1 The 4M Algorithm……Page 365
3.2 Bounds on the Tail Probability for Markov Chains……Page 366
3.3 Kullback-Leibler Divergence Rates Between Markov Models……Page 368
4.1 Introduction to Genomics……Page 370
4.2 The Gene Finding Problem……Page 371
4.3 Computational Results……Page 373
References……Page 377
1 Introduction……Page 379
2 Regulation of Molecule Numbers……Page 380
2.1 Feedback Channels……Page 382
2.2 Limitations Due to Feedback Capacity……Page 384
2.3 Limitations Due to Delay……Page 385
3 Feedback Networks……Page 387
3.1 Modules and Protocols……Page 390
3.2 Example: Vehicle Platooning……Page 392
4 Conclusions……Page 393
References……Page 394
1 Introduction……Page 396
2 Deterministic Models……Page 397
3 Deterministic Linear Dynamical Systems……Page 399
4 Controllability……Page 403
5 The MPUM……Page 405
6 Subspace ID……Page 409
7 Latency Minimization……Page 413
8 Interpretations of Probability……Page 416
9 Stochastics in SYSID……Page 420
References……Page 422
1 Introduction……Page 424
2 Absolute Bound of Complexity……Page 428
3 Proof of Main Theorem……Page 429
4 Combination with Deterministic Methods……Page 433
5 Conclusions……Page 434
References……Page 435
back-matter.pdf……Page 437