Decentralized Control and Filtering in Interconnected Dynamical Systems

1.1 Overview......Page 1
1.1.1 Information structure......Page 3
1.1.2 System representation......Page 4
1.1.3 Hierarchical systems......Page 7
1.1.4 Structure of interconnections......Page 8
1.1.5 Revived challenges......Page 10
1.2.1 Methodology......Page 12
1.2.2 Chapter organization......Page 13
1.3 Some Notes......Page 15
2.1.1 Euclidean space......Page 17
2.1.2 Norms of vectors......Page 18
2.1.3 Convex sets......Page 19
2.1.5 Function norms......Page 20
2.2 Calculus and Algebra of Matrices......Page 21
2.2.1 Fundamental subspaces......Page 22
2.2.2 Calculus of vector-matrix functions of a scalar......Page 23
2.2.3 Derivatives of vector-matrix products......Page 24
2.2.5 Trace properties......Page 26
2.2.6 Partitioned matrices......Page 28
2.2.7 Matrix inversion lemma......Page 29
2.2.8 Singular value decomposition......Page 30
2.3 Directed Graphs......Page 31
2.4 Notes and References......Page 33
3. Historical Perspective and Scope......Page 34
3.2 Decomposition-Coordination Methods......Page 35
3.2.1 Hierarchical structures......Page 37
3.2.2 Decentralized control......Page 38
3.3.1 Local-level optimization......Page 39
3.4 Decentralized Nonlinear Systems......Page 43
3.4.1 Diagonal dominance condition......Page 45
3.4.2 Static controller design......Page 46
3.4.3 Illustrative example 3.1......Page 49
3.5 Nominally Linear Systems—Continuous Case......Page 50
3.5.1 Decentralized control......Page 53
3.5.2 Two-level control......Page 54
3.5.3 Illustrative example 3.2......Page 56
3.6 Linear Systems......Page 60
3.7 A Perturbational Approach......Page 65
3.7.1 Multilevel state regulation......Page 69
3.7.2 Generalized scheme......Page 72
3.7.3 Illustrative example 3.4......Page 76
3.8 Observation and Estimation......Page 78
3.8.2 Observation scheme I......Page 79
3.8.3 Observation scheme II......Page 81
3.8.4 Estimation scheme......Page 82
3.9 Interconnected Discrete-Time Systems......Page 86
3.9.1 Mode separation indiscrete systems......Page 88
3.10.1 State feedback design......Page 91
3.10.3 Illustrative example 3.5......Page 92
3.10.5 Design algorithm II......Page 94
3.10.6 Observer-based control design......Page 95
3.10.8 Illustrative example 3.6......Page 96
3.10.9 Decentralized state reconstruction......Page 101
3.10.10 Illustrative example 3.7......Page 103
3.10.11 Linear quadratic control design......Page 104
3.10.12 Illustrative example 3.8......Page 109
3.11 Applications......Page 110
3.11.2 Liquid-metal cooled reactor......Page 111
3.11.3 Boiler system......Page 114
3.11.4 Hydraulic system with electronic test gear......Page 122
3.12 ProblemSet I......Page 123
3.13 Notes and References......Page 128
4. Decentralized Servomechanism System......Page 130
4.2 A Class of Large-Scale Systems......Page 131
4.3.1 Fixed modes......Page 133
4.3.2 Decentralized fixed modes......Page 139
4.4.1 Illustrative example 4.1......Page 140
4.4.2 Illustrative example 4.2......Page 142
4.4.3 Illustrative example 4.3......Page 143
4.5 Decentralized Regulators......Page 144
4.5.1 The robust decentralized servomechanism problem......Page 145
4.5.2 The robust decentralized controller......Page 147
4.5.3 Decentralized controller for interconnected systems......Page 149
4.5.4 Illustrative example 4.4......Page 151
4.6 Hierarchically Structured Servomechanism......Page 153
4.6.1 Decentralized controller structure......Page 157
4.6.2 Illustrative example 4.5......Page 159
4.6.3 Illustrative example 4.6......Page 160
4.7 Problem Set II......Page 161
4.8 Notes and References......Page 163
5. Overlapping Control......Page 165
5.1.1 Decoupled subsystems......Page 166
5.1.3 Transformations......Page 168
5.1.4 Illustrative example 5.1......Page 170
5.2 Feedback Control Design......Page 171
5.2.1 Linear-quadratic control......Page 172
5.2.2 Change of basis......Page 174
5.2.3 Improved expansion-contraction......Page 175
5.2.4 Particular selection......Page 179
5.2.5 Illustrative example 5.2......Page 181
5.3 LMI-Based Overlapping Control......Page 185
5.3.1 Design procedure......Page 187
5.3.2 Illustrative example 5.3......Page 188
5.4 Application to Unmanned Aerial Vehicles......Page 189
5.5 Problem Set III......Page 196
5.6 Notes and References......Page 199
6.1 Introduction......Page 200
6.2 Linear Interconnected Systems: Continuous-Time......Page 201
6.2.1 Local delay-dependent analysis......Page 203
6.2.2 Linear polytopic systems......Page 209
6.2.3 Illustrative example 6.1......Page 211
6.2.4 State feedback stabilization......Page 212
6.2.5 Illustrative example 6.2......Page 215
6.3.1 Problem statement......Page 216
6.3.2 Local delay-dependent analysis......Page 217
6.3.3 State feedback stabilization......Page 223
6.3.4 Illustrative example 6.3......Page 226
6.4 Interconnected Discrete-Time-Delay Systems......Page 228
6.4.1 Model description and preliminaries......Page 229
6.4.2 Subsystem stability......Page 231
6.4.3 State feedback design......Page 235
6.4.4 Bounded state feedback design......Page 236
6.4.5 Resilient state feedback design......Page 237
6.4.6 Output feedback stabilization......Page 241
6.4.7 Resilient output feedback stabilization......Page 244
6.4.8 Illustrative example 6.4......Page 247
6.5 Overlapping Control......Page 251
6.5.1 Systems and inclusions......Page 254
6.5.2 Inclusion of linear quadratic costs......Page 256
6.5.3 Guaranteed cost control......Page 261
6.5.4 Overlapping control design......Page 263
6.5.5 Illustrative example 6.5......Page 266
6.6 Problem Set IV......Page 268
6.7 Notes and References......Page 272
7.1 Interconnected Continuous Systems......Page 274
7.1.1 Problem description......Page 276
7.1.2 Actuator failure model......Page 277
7.1.3 State-feedback reliable design......Page 278
7.1.4 Feedback gains......Page 285
7.1.5 Interconnected uncertain systems......Page 286
7.1.6 Static output-feedback reliable design......Page 288
7.1.7 Illustrative example 7.1......Page 290
7.2 Application to Multi-Area Power Systems......Page 293
7.2.1 Single-area AGC model......Page 297
7.2.2 Simulation results......Page 298
7.2.3 Reliable control against sensor failures......Page 302
7.2.4 State-feedback reliable design......Page 304
7.2.5 Dynamic output-feedback reliable design......Page 311
7.2.6 Illustrative example 7.2......Page 315
7.3.1 Problem formulation......Page 318
7.3.2 Failure model......Page 319
7.3.3 State-feedback reliable design......Page 320
7.3.4 Illustrative example 7.3......Page 328
7.4 Reliable Control of Symmetric Composite Systems......Page 332
7.4.1 Problem formulation......Page 334
7.4.2 Decentralized H∞ control......Page 336
7.4.3 Controller design......Page 340
7.4.5 Illustrative example 7.5......Page 343
7.4.7 Control input failures......Page 344
7.4.8 General failures......Page 346
7.4.11 Illustrative example 7.8......Page 348
7.5 Problem Set V......Page 350
7.6 Notes and References......Page 354
8.1 Introduction......Page 355
8.2 Problem Statement......Page 356
8.3 Resilient Decentralized Stabilization......Page 358
8.3.1 Resilient state feedback......Page 359
8.3.2 Resilient static output feedback......Page 363
8.3.3 Resilient dynamic output feedback......Page 370
8.3.4 Illustrative example 8.1......Page 379
8.3.5 Illustrative example 8.2......Page 380
8.3.7 Illustrative example 8.4......Page 381
8.4 Resilient Overlapping Control......Page 383
8.4.1 Feedback problem formulation......Page 386
8.4.2 LMI control design......Page 389
8.4.3 Application of the inclusion principle......Page 390
8.4.4 Overlapping state feedback......Page 396
8.4.5 Illustrative example 8.5......Page 398
8.5 Resilient Stabilization for Discrete Systems......Page 400
8.5.1 Problem statement......Page 401
8.5.2 Subsystem stability......Page 403
8.5.3 State feedback design......Page 405
8.5.4 Bounded state feedback design......Page 406
8.5.5 Resilient state feedback design......Page 407
8.5.6 Output feedback stabilization......Page 411
8.5.7 Resilient output feedback stabilization......Page 413
8.5.8 Illustrative example 8.6......Page 417
8.6 Problem Set VI......Page 419
8.7 Notes and References......Page 422
9.1 Robust Sliding-Mode Control......Page 423
9.1.1 Introduction and preliminaries......Page 424
9.1.2 System description......Page 425
9.1.3 Stability analysis......Page 427
9.1.4 Decentralized sliding-mode control......Page 430
9.1.5 Illustrative example 9.1......Page 433
9.2 Delay-Dependent Sliding-Mode Control......Page 436
9.2.1 System description......Page 437
9.2.2 Stability analysis......Page 440
9.2.3 Reachability analysis......Page 445
9.2.4 Illustrative example 9.2......Page 448
9.3 Problem Set VII......Page 450
9.4 Notes and References......Page 453
10.1 Introduction......Page 455
10.2 Problem Statement......Page 456
10.3 Robust Subsystem Filters......Page 457
10.3.1 Robust l ∞ filter......Page 458
10.3.2 Illustrative example 10.1......Page 463
10.4 Resilient Subsystem Filters......Page 464
10.4.1 Resilient l ∞ filter......Page 466
10.4.2 Illustrative example 10.2......Page 469
10.5 Problem Set VIII......Page 471
10.6 Notes and References......Page 472
11.1 Decentralized Kalman Filtering......Page 474
11.1.1 Basis of filtering method......Page 475
11.1.2 The algebraic structure......Page 477
11.1.3 Application to multimachine system......Page 480
11.2 Decentralized Fault Detection......Page 484
11.2.1 System model......Page 485
11.2.2 Overlapping decomposition......Page 486
11.2.3 Fault detection technique......Page 488
11.2.4 Simulation results......Page 490
11.3 Problem Set IX......Page 502
11.4 Notes and References......Page 504
12.1 Processing Aspects......Page 505
12.2.2 Weakly coupled subsystems......Page 506
12.2.3 Strongly coupled subsystems......Page 507
12.2.5 Design of decentralized systems......Page 508
12.2.6 Application aspects......Page 509
13.1.1 Practical stabilizability......Page 511
13.1.2 Razumikhin stability......Page 512
13.2.2 Inequality 2......Page 514
13.2.4 Inequality 4 (Schur complements)......Page 515
13.2.5 Inequality 5......Page 517
13.3 Lemmas......Page 518
13.4.1 Basics......Page 522
13.4.2 Some standard problems......Page 523
13.4.3 The S-procedure......Page 525
13.6.1 Inverse of block matrices......Page 526
13.6.2 Matrix inversion lemma......Page 527
13.7 Some Discrete Lyapunov-Krasovskii Functionals......Page 528
13.8 Additional Inequalities......Page 530
Bibliography......Page 534