Directions in Mathematical Systems Theory and Optimization

Directions in Mathematical Systems Theory and Optimization......Page 3
Preface......Page 6
Contents......Page 7
front-matter......Page 1
1.1 Introduction......Page 12
1.2 Examples of Systems with Lebesgue Sampling......Page 13
1.3 A Simple Example......Page 15
1.4 A First Order System......Page 17
1.5 Conclusions......Page 22
1.6 References......Page 23
02......Page 25
2.2 Problem Formulation......Page 26
2.3 Frequency Domain and Approximation......Page 27
2.4 Instantaneous Total Energy and Damping......Page 31
2.5 Computational Results......Page 32
2.7 References......Page 36
3.1 Introduction......Page 37
3.2 Linear Random Functionals......Page 38
3.3 Description of the Model and Statement of the Problem......Page 40
3.4 Obtaining the Best Estimate......Page 44
3.5 Final Form. Decoupling Theory......Page 48
3.6 References......Page 49
04......Page 50
4.2 Notation and Definitions......Page 51
4.3 Connections to Ergodic Control......Page 55
4.4 References......Page 58
05......Page 59
5.1 Introduction......Page 60
5.2 The Case of a SISO System......Page 61
5.3 A Numerical Example of Take-Off and Landing......Page 65
5.4 Remarks on the Internal Model Principle......Page 70
5.5 The Case of a MIMO System......Page 71
5.6 References......Page 77
06......Page 79
6.1 Introduction......Page 80
6.2 Main Results......Page 81
6.3 References......Page 92
07......Page 93
7.1 Introduction......Page 94
7.2 Oblique Projections......Page 95
7.3 Notations and Basic Assumptions......Page 97
7.4 Oblique Markovian Splitting Subspaces......Page 100
7.5 Acausality of Realizations with Feedback......Page 108
7.6 Scattering Representations of Oblique Markovian Splitting Subspaces......Page 113
7.7 Stochastic Realization in the Absence of Feedback......Page 117
7.8 Reconciliation with Stochastic Realization Theory......Page 128
7.10 References......Page 132
08......Page 135
8.2 A Solution......Page 136
8.3 An Application......Page 137
8.4 References......Page 141
09......Page 142
9.2 Structured Covariances......Page 143
9.3 Sample Covariances and the Approximation Problem......Page 144
9.4 Concluding Remarks......Page 146
9.5 References......Page 147
10......Page 148
10.1 Weighted Recursive Prediction Error Identification......Page 149
10.2 A Risk-Sensitive Criterion......Page 151
10.3 The Minimization of J(K)......Page 153
10.4 Alternative Expressions for J(K)......Page 156
10.5 Multivariable Systems......Page 161
10.6 Bibliography......Page 164
11......Page 165
11.2 Autonomous Linear Systems......Page 166
11.3 Exact Input Tracking......Page 169
11.4 Output Fusion for Input Tracking......Page 172
11.5 Concluding Remarks......Page 177
11.6 References......Page 178
12......Page 179
12.1 Introduction......Page 180
12.2 Proof of the Main Theorem......Page 183
12.3 Conclusions......Page 187
12.4 References......Page 188
13......Page 189
13.1 Introduction......Page 190
13.2 System Description and Compensator Structure......Page 191
13.3 Application of H-infinity Control to Systems with Time Delay......Page 192
13.4 Conclusion......Page 195
Appendix......Page 196
14......Page 199
14.2 The Basic Problem and the Cost Functional......Page 200
14.3 Guaranteed (Set-Membership) Estimation......Page 201
14.4 Control Synthesis for the Set-Valued Control System......Page 204
14.5 Solution through Duality Techniques......Page 205
14.6 References......Page 208
15......Page 209
15.2 Curve Fitting......Page 210
15.3 Linear Dynamic Models......Page 213
15.4 Fitting the Frequency Function Curve by Local Methods......Page 216
15.5 Fitting the Frequency Function by Parametric Methods......Page 217
15.7 References......Page 220
16......Page 222
16.1 Introduction......Page 223
16.2 Maximal Real Part Model Reduction......Page 224
16.3 H-Infinity Modeling Error Bounds......Page 228
16.4 Minor Improvements and Numerical Experiments......Page 229
17......Page 232
17.1 Introduction: Schrödinger’s Problem......Page 233
17.2 Elements of Nelson-Föllmer Kinematics of Finite Energy Diffusions......Page 234
17.3 Schrödinger Bridges......Page 236
17.4 Elements of Nelson’s Stochastic Mechanics......Page 237
17.5 Quantum Schrödinger Bridges......Page 238
17.8 References......Page 240
18......Page 244
18.1 Introduction......Page 245
18.2 Active Contours and Diffusion Tensor Imaging......Page 246
18.4 Bibliography......Page 250
19......Page 253
19.2 Matrix Norms and Preliminaries......Page 254
19.3 Solution Set of Perturbed Linear Algebraic Equations......Page 256
19.4 Nonsingularity Radius......Page 258
19.5 Real Pseudospectrum......Page 259
19.7 Conclusions......Page 262
19.8 References......Page 263
20......Page 265
20.2 Preliminaries......Page 266
20.3 Homogeneous Density Functions for Homogeneous Systems......Page 269
20.4 Perturbations by Higher and Lower Order Terms......Page 276
20.6 References......Page 277
21......Page 279
21.1 Introduction......Page 280
21.2 Infinite-Dimensional Linear Systems......Page 281
21.3 Passive and Conservative Scattering and Impedance Systems......Page 284
21.4 Flow-Inversion......Page 288
 21.5 The Diagonal Transform......Page 293
21.6 References......Page 295
22......Page 297
22.1 Introduction......Page 298
22.2 Preliminaries......Page 302
22.3 The Finite-Dimensional Theorem......Page 305
22.4 The Infinite-Dimensional Theorem......Page 307
22.5 Second-Order Open Mapping Theorems......Page 312
22.6 References......Page 319
23......Page 321
23.2 Previous Work on Integrability Conditions......Page 322
23.3 New Integrability Conditions......Page 327
23.4 Applications of the New Conditions......Page 333
23.5 Conclusions......Page 334
23.6 References......Page 335
24......Page 336
24.1 Introduction and Problem Formulation......Page 337
24.2 Orthonormal Rational Functions......Page 339
24.3 Least Squares Estimation......Page 341
24.4 The Covariance Extension Problem......Page 344
24.6 References......Page 346
25......Page 348
25.1 Introduction......Page 349
25.2 The System Equations......Page 350
25.3 The Controllability and Observability Gramians......Page 351
25.4 Balanced State Representation......Page 354
25.5 Comments......Page 356
25.6 Appendix......Page 358
25.7 References......Page 360
26......Page 361
26.2 A Method for Solving Constrained Linear-Quadratic Problems (Abstract Theory)......Page 362
26.3 Linear-Quadratic Deterministic Infinite-Horizon Constrained Optimization Problem......Page 367
26.4 Linear-Quadratic Stochastic Infinite-Horizon Optimization Problem with White-Noise Disturbance......Page 374
26.5 Appendix. (Discrete KYP-Lemma.) The Frequency-Domain Method to Solve Discrete Lur’e-Riccati Equations......Page 380
26.6 References......Page 383
Author List......Page 385