Fundamental Limitations in Filtering and Control

Preface......Page 4
Contents......Page 8
Part I: Introduction......Page 14
1.1 Introduction......Page 16
1.2 Performance Limitations in Dynamical Systems......Page 19
1.3 Time Domain Constraints......Page 22
1.4 Frequency Domain Constraints......Page 31
1.5 A Brief History......Page 32
1.6 Summary......Page 33
Notes and References......Page 34
Part II: Limitations in LinearControl......Page 36
2 Review of General Concepts......Page 38
2.1 Linear Time-Invariant Systems......Page 39
2.2 Feedback Control Systems......Page 44
2.3 Two Applications of Complex Integration......Page 49
Notes and References......Page 58
3.1 Bode Integral Formulae......Page 60
3.2 The Water-Bed Effect......Page 75
3.3 Poisson Integral Formulae......Page 77
3.4 Discrete Systems......Page 87
3.5 Summary......Page 96
Notes and References......Page 97
4.1 Interpolation Constraints......Page 98
4.2 Bode Integral Formulae......Page 100
4.3 Poisson Integral Formulae......Page 111
4.4 Discrete Systems......Page 126
Notes and References......Page 129
5.1 Periodic Discrete-Time Systems......Page 132
5.2 Sensitivity Functions......Page 135
5.3 Integral Constraints......Page 137
5.4 Design Interpretations......Page 139
Notes and References......Page 145
6 Extensions to Sampled-Data Systems......Page 148
6.1 Preliminaries.......Page 149
6.2 Sensitivity Functions......Page 154
6.3 Interpolation Constraints......Page 158
6.4 Poisson Integral formulae......Page 163
6.5 Example: Robustness of Discrete Zero Shifting......Page 169
Notes and References......Page 171
Part III: Limitations in LinearFiltering......Page 174
7.1 General Filtering Problem......Page 176
7.2 Sensitivity Functions......Page 178
7.3 Bounded Error Estimators......Page 185
7.4 Summary......Page 189
Notes and References......Page 190
8.1 Interpolation Constraints......Page 192
8.2 Integral Constraints......Page 194
8.3 Design Interpretations......Page 197
8.4 Examples: Kalman Filter......Page 202
8.5 Example: Inverted Pendulum......Page 206
8.6 Summary......Page 208
Notes and References......Page 209
9 MIMO Filtering......Page 210
9.1 Interpolation Constraints......Page 211
9.2 Poisson Integral Constraints......Page 212
9.3 The Cost of Diagonalization......Page 215
9.4 Application to Fault Detection......Page 218
Notes and References......Page 221
10.1 General Prediction Problem......Page 222
10.2 Sensitivity Functions......Page 225
10.3 BEE Derived Predictors......Page 226
10.4 Interpolation Constraints......Page 227
10.5 Integral Constraints......Page 230
10.6 Effect of the Prediction Horizon......Page 232
Notes and References......Page 239
11.1 General Smoothing Problem......Page 240
11.2 Sensitivity Functions......Page 243
11.3 BEE Derived Smoothers......Page 244
11.4 Interpolation Constraints......Page 245
11.5 Integral Constraints......Page 247
11.6 Sensitivity Improvement of the Optimal Smoother......Page 250
11.7 Summary......Page 253
Notes and References......Page 254
Part IV: Limitations in NonlinearControl and Filtering......Page 256
12.1 Nonlinear Operators......Page 258
12.2 Nonlinear Cancelations......Page 262
Notes and References......Page 265
13.1 Review of Linear Sensitivity Relations......Page 266
13.2 A Complementarity Constraint......Page 267
13.3 Sensitivity Limitations......Page 269
13.4 The Water-Bed Effect......Page 271
13.5 Sensitivity and Stability Robustness......Page 273
13.6 Summary......Page 275
Notes and References......Page 276
14.1 A Complementarity Constraint......Page 278
14.2 Bounded Error Nonlinear Estimation......Page 281
14.3 Sensitivity Limitations......Page 282
Notes and References......Page 284
Part V: Appendices......Page 286
A.1 Functions, Domains and Regions......Page 288
A.2 Complex Differentiation......Page 289
A.3 Analytic functions......Page 291
A.4 Complex Integration......Page 294
A.5 Main Integral Theorems......Page 302
A.6 The Poisson Integral Formula......Page 311
A.7 Power Series......Page 317
A.8 Singularities......Page 323
A.9 Integration of Functions with Singularities......Page 328
A.10 The Maximum Modulus Principle......Page 334
A.11 Entire Functions......Page 335
Notes and References......Page 337
B.1 Proofs for Chapter 4......Page 338
B.2 Proofs for Chapter 6......Page 345
C: The Laplace Transform of the Prediction Error......Page 352
D: Least Squares Smoother Sensitivities for Large......Page 356
Bibliography......Page 360
Index......Page 370