Decentralized systems with design constraints

✍ Scribed by Mahmoud, Magdi S

• Publisher: Springer
• Year: 2011
• Tongue: English
• Leaves: 565
• Category: Library

✦ Synopsis

Decentralized Control and Filtering provides a rigorous framework for examining the analysis, stability and control of large-scale systems, addressing the difficulties that arise because dimensionality, information structure constraints, parametric uncertainty and time-delays. This monograph serves three purposes: it reviews past methods and results from a contemporary perspective; it examines presents trends and approaches and to provide future possibilities; and it investigates robust, reliable and/or resilient decentralized design methods based on a framework of linear matrix inequalities. As well as providing an overview of large-scale systems theories from the past several decades, the author presents key modern concepts and efficient computational methods. Representative numerical examples, end-of-chapter problems, and typical system applications are included, and theoretical developments and practical applications of large-scale dynamical systems are discussed in depth.

✦ Table of Contents

9.1.2 Norms of Vectors......Page 2
9.1.6 Function Norms......Page 6
9.2.1 Fundamental Subspaces......Page 9
Acknowledgements......Page 10
9.2.12 Kronecker Product and vec......Page 17
Cover......Page 1
Decentralized Systems with Design Constraints......Page 3
9.1.4 Convex Sets......Page 4
8.2.1 Decentralized Feedback Control for Nonlinear Systems......Page 5
Preface......Page 7
8.3 Application to Decentralized Control......Page 8
Contents......Page 11
9.2.7 Power of a Square Matrix......Page 14
9.2.11 Trace Properties......Page 16
Abbreviations......Page 18
9.2.15 Strengthened Version of Lemma of Lyapunov......Page 19
1.1 Introduction......Page 21
1.2 Feedback Control......Page 22
1.2.2 System Representation......Page 24
References......Page 29
9.7.1 Lyapunov-Razumikhin Theorem......Page 30
9.7.3 Halany Theorem......Page 33
8.4.5 Simulation Example 8.5......Page 40
8.4.6 Tracking Behavior......Page 42
2.2.1.2 Reduced Order Observer......Page 44
2.2.1.3 Important Special Case......Page 46
2.2.5 Dynamic Control Design......Page 52
8.6.3 The Decentralized Adaptive Problem......Page 55
7.3.4 Results in the Finite Horizon Case......Page 56
2.3.1 Construction Procedure......Page 60
8.7.1 The Digital Redesign Methodology......Page 61
8.7.4 Simulation Example 8.7......Page 68
5.5.6 Simulation Example 5.6......Page 69
2.4 Decentralized Tracking: Class III......Page 72
2.4.2 Design Procedure......Page 76
2.7 Notes and References......Page 80
References......Page 81
9.2.9 Eigenvalues and Eigenvectors of a Square Matrix......Page 15
1.2.1 Information Structure......Page 23
1.2.3 Team Problems......Page 25
2.1.2.1 System Description......Page 34
7.2.6 Simulation Example 7.1......Page 35
References......Page 36
2.1.3.1 System Description......Page 37
2.2 Dynamic Output Feedback: Class I......Page 38
6.8.5 Some Properties......Page 43
3.4.7 L2-Gain Disturbance Attenuation......Page 45
8.4.7 Simulation Example 8.6......Page 47
2.2.3 Simulation Example 2.2......Page 49
3.6.1 Introduction......Page 62
2.3.2 Recursive Design......Page 63
3.6.4 Robust Performance Analysis......Page 67
5.6 Notes and References......Page 73
3.6.6 Simulation Results......Page 77
References......Page 84
9.2.4 Derivatives of Vector-Matrix Products......Page 12
1.2.5 Hierarchical Systems......Page 26
1.3 Outline of the Book......Page 27
1.3.1 Methodology......Page 28
2.2.1 Observer-Based Control Design......Page 39
9.2.5 Positive Definite and Positive Semidefinite Matrices......Page 13
9.2.16 The Singular Value Decomposition......Page 20
2.2.2 Simulation Example 2.1......Page 48
5.4.1 Introduction......Page 50
2.2.4 Simulation Example 2.3......Page 51
5.4.6 Simulation Example 5.5......Page 58
7.3.6 Appendix......Page 64
7.4 Notes and References......Page 65
2.4.1 Partially Decentralized Observer......Page 74
2.1.1.1 System Description......Page 32
2.2.7 Simulation Example 2.4......Page 59
2.1 Classes of Nonlinear Interconnected Systems......Page 31
2.2.1.1 Full Order Observer......Page 41
8.7.3 Incorporating Optimal Tracker......Page 66
2.2.6 Robust Decentralized Design......Page 54
8.6.3.1 A Model-Reference Adaptive Controller......Page 57
References......Page 75
2.3.3 Simulation Example 2.5......Page 70
2.4.3 Design Results......Page 82
2.5 Decentralized Guaranteed Cost Control......Page 85
2.5.1 Analysis of Robust Performance......Page 86
2.5.2 Including Input Delays......Page 90
2.5.3 Decentralized Design Results......Page 91
2.6.1 Introduction......Page 98
2.6.2 Problem Formulation and Assumptions......Page 99
2.6.3 Robust Control Design......Page 102
2.6.4 Simulation Example 2.7......Page 106
2.6.5 Proof of Lemma 2.8......Page 110
References......Page 111
3.1 Introduction......Page 115
3.1.1 System Description......Page 116
3.1.2 Robust Control Design......Page 118
3.1.3 Recursive Method......Page 121
3.1.4 Simulation Example 3.1......Page 129
3.2.1 Introduction......Page 132
3.3 Decentralized Hinfty Control......Page 133
3.3.1 The Local Disturbance Problem......Page 137
3.3.2 Results for Non-minimum Phase Systems......Page 139
3.4 Global Inverse Control of Nonlinear Systems......Page 143
3.4.1 Disturbance Attenuating Trackers......Page 147
3.4.2 System Description......Page 148
3.4.3 Output Feedback Tracking......Page 149
3.4.4 Partially Decentralized Observer......Page 150
3.4.5 Controller Design Procedure......Page 151
Step j.1.......Page 152
Step j.k (2 <=k <=nj).......Page 154
3.4.6 Control Design Results......Page 157
3.4.7 L2-Gain Disturbance Attenuation......Page 159
3.5 Application to Power Systems......Page 160
3.5.1 Power System Model......Page 161
3.5.2 Robust Stabilization......Page 163
3.5.3 Simulation Results......Page 169
3.6.1 Introduction......Page 176
3.6.2 Dynamical Model of Multimachine Power System......Page 177
3.6.4 Robust Performance Analysis......Page 181
3.6.5 Guaranteed Cost Controller Design......Page 187
3.6.6 Simulation Results......Page 191
References......Page 198
4.1 Introduction......Page 202
4.2.1 Introduction......Page 203
4.2.2 Problem Statement......Page 204
4.2.3 Decentralized Stabilization......Page 207
4.2.4 Simulation Example 4.1......Page 210
4.3 Resilient Stabilization of Interconnected Networked Systems......Page 211
4.3.1 Introduction......Page 212
4.3.2 Problem Formulation......Page 213
4.3.3 Resilient Observer-Based Control......Page 215
4.3.4 Augmented Closed-Loop System......Page 217
4.3.5 Delay-Dependent Subsystem Stability......Page 218
4.3.6 Simulation Example 4.2......Page 225
4.4.1 Introduction......Page 227
4.4.2 Problem Formulation......Page 228
4.4.3 Review Results......Page 229
4.4.4 Main Results......Page 231
4.5 Notes and References......Page 240
5.1 Decentralized Quantized Control I: Continuous Systems......Page 245
5.1.1 Problem Statement......Page 246
5.1.2 Local Quantizer Description......Page 247
5.1.3 Static Output-Feedback Design......Page 248
5.1.4 Quantized Output-Feedback Design......Page 254
5.1.5 Simulation Example 5.1......Page 257
5.1.6 Polytopic Systems......Page 258
5.1.7 Delay-Free Systems......Page 260
5.2 Decentralized Quantized Control II: Continuous Systems......Page 261
5.2.1 Problem Statement......Page 262
5.2.2 A Class of Local Quantizers......Page 264
5.2.3 Quantized Output-Feedback Design......Page 265
5.2.4.1 Delay-Free Systems......Page 270
5.2.4.2 Single Time-Delay Systems......Page 271
5.2.4.3 Single Systems......Page 273
5.3.1 Introduction......Page 277
5.3.2 Problem Description......Page 278
5.3.3 Local Quantizers......Page 279
5.3.4 Static Output-Feedback Design......Page 280
5.3.5 Quantized Output-Feedback Design......Page 283
5.3.6 Special Cases......Page 287
5.3.7 Simulation Example 5.3......Page 290
5.3.8 Simulation Example 5.4......Page 292
5.4 Decentralized Quantized Control II: Discrete Systems......Page 293
5.4.1 Introduction......Page 294
5.4.2 Problem Statement......Page 295
5.4.4 Quantized Feedback Design......Page 296
5.4.5 Special Cases......Page 300
5.4.6 Simulation Example 5.5......Page 302
5.5.1 Introduction......Page 305
5.5.3 Local Static Control Function......Page 308
5.5.4 Closed-Loop Stabilization......Page 309
5.5.5 Local Dynamic Control Function......Page 312
5.5.6 Simulation Example 5.6......Page 313
5.6 Notes and References......Page 317
References......Page 318
6.1 Introduction......Page 320
6.2 A Model of Communication Networks......Page 322
6.3 Problem Formulation......Page 323
6.3.1 A Network Example......Page 324
6.4.1 Delay-Dependent Hinfty Unconstrained Control Design......Page 325
6.4.2 Delay-Dependent Hinfty Design......Page 326
6.5.1 Decentralized Dynamic Model......Page 327
6.5.2 Decentralized Robust Routing Controller: Unconstrained Case......Page 328
6.5.3 Decentralized Robust Routing Controller: Constrained Case......Page 331
6.6.1 Simulation Example 6.1......Page 332
6.6.2 Simulation Example 6.2......Page 335
6.7.1 Proof of Theorem 6.1......Page 337
6.7.2 Proof of Theorem 6.2......Page 339
6.7.3 Proof of Theorem 6.3......Page 340
6.7.4 Proof of Theorem 6.4......Page 344
6.8.1 Routing Algorithms......Page 345
6.8.2 Network Dynamics and Assumptions......Page 347
6.8.3 Routing Control Algorithm......Page 351
6.8.4 Selection of the Feedback Matrix......Page 358
6.8.5 Some Properties......Page 362
6.8.6 Simulation Examples......Page 370
Routing Controller Obtained.......Page 371
6.9 Notes and References......Page 378
References......Page 380
7.1 Control for Markovian Jump Systems......Page 382
7.1.1 Introduction......Page 383
7.1.3 Hinfty-State Feedback Controller......Page 390
7.1.4 Robust Hinfty-Control Results......Page 395
7.2.2 Problem Statement......Page 403
7.2.3 Local Subsystem Stability......Page 405
7.2.4 Hinfty State-Feedback Synthesis......Page 410
7.2.5 Dynamic Output-Feedback Control......Page 412
7.2.6 Simulation Example 7.1......Page 416
7.3 Hinfty Control by Averaging and Aggregation......Page 420
7.3.1 Introduction......Page 421
7.3.2 Problem Formulation......Page 422
7.3.3 Results in the Infinite-Horizon Case......Page 427
7.3.4 Results in the Finite Horizon Case......Page 437
7.3.5 Simulation Example 7.2......Page 442
7.3.6 Appendix......Page 445
7.4 Notes and References......Page 446
References......Page 447
Chapter 8: Decentralized Adaptive Control......Page 450
8.1 Introduction......Page 451
8.2.1 Decentralized Feedback Control for Nonlinear Systems......Page 454
8.3 Application to Decentralized Control......Page 457
8.3.1 Simulation Example 8.1......Page 460
8.3.2 Simulation Example 8.2......Page 463
8.4 Adaptive Techniques for Interconnected Nonlinear Systems......Page 465
8.4.1 A Class of Interconnected Nonlinear Systems......Page 466
8.4.2 Decentralized Adaptive Design......Page 468
8.4.3 Simulation Example 8.3......Page 485
8.4.4 Simulation Example 8.4......Page 488
8.4.5 Simulation Example 8.5......Page 489
8.4.6 Tracking Behavior......Page 491
8.4.7 Simulation Example 8.6......Page 496
8.5.1 Proof of Theorem 2.1......Page 500
8.5.2 Proof of Proposition 8.1......Page 501
8.6.1 Introduction......Page 503
8.6.2 The Decentralized Adaptive Control Design......Page 504
8.6.3.1 A Model-Reference Adaptive Controller......Page 506
8.7.1 The Digital Redesign Methodology......Page 510
8.7.2 An Improved Redesign Adaptive Controller......Page 512
8.7.3 Incorporating Optimal Tracker......Page 515
8.7.4 Simulation Example 8.7......Page 517
8.8 Notes and References......Page 521
References......Page 524
9.1.1 Vector Spaces......Page 527
9.1.2 Norms of Vectors......Page 528
Induced norms of matrices......Page 529
9.1.4 Convex Sets......Page 530
9.1.6 Function Norms......Page 532
9.1.7 Mean Value Theorem......Page 533
9.2.1 Fundamental Subspaces......Page 535
9.2.2 Change of Basis and Invariance......Page 536
9.2.3 Calculus of Vector-Matrix Functions of a Scalar......Page 537
9.2.4 Derivatives of Vector-Matrix Products......Page 538
9.2.5 Positive Definite and Positive Semidefinite Matrices......Page 539
9.2.6 Matrix Ellipsoid......Page 540
9.2.8 Exponential of a Square Matrix......Page 541
9.2.10 The Cayley-Hamiltonian Theorem......Page 542
9.2.12 Kronecker Product and vec......Page 543
9.2.13 Partitioned Matrices......Page 544
9.2.14 The Matrix Inversion Lemma......Page 545
9.2.16 The Singular Value Decomposition......Page 546
9.3.1 Bounding Inequality A......Page 547
9.3.2 Bounding Inequality B......Page 548
9.3.3 Bounding Inequality C......Page 549
9.4 Gronwall-Bellman Inequality......Page 550
9.5 Schur Complements......Page 551
9.6 Lemmas......Page 552
9.7.1 Lyapunov-Razumikhin Theorem......Page 556
9.7.2 Lyapunov-Krasovskii Theorem......Page 557
9.7.3 Halany Theorem......Page 559
9.7.5 Some Discrete Lyapunov-Krasovskii Functionals......Page 560
9.8 Notes and References......Page 562
Index......Page 563