Handbook of Hybrid Systems Control: Theory, Tools, Applications

Half-title......Page 3
Title......Page 5
Copyright......Page 6
Content......Page 7
List of contributors......Page 9
Preface......Page 15
Notation......Page 18
Part I Theory......Page 19
1 Introduction to hybrid systems......Page 21
1.1.1 Three reasons to study hybrid systems......Page 22
1.1.2 Behavior of hybrid systems......Page 24
1.1.3 Hybrid dynamical phenomena......Page 27
1.2.1 Model ingredients......Page 32
1.2.2 Model behavior......Page 34
1.3.1 Two-tank system......Page 35
1.3.2 Automatic gearbox......Page 40
1.3.3 DC-DC converter......Page 44
Bibliographical notes......Page 48
2 Survey of modeling, analysis, and control of hybrid systems......Page 49
2.1.1 Overview......Page 51
2.1.3 Switched systems......Page 53
2.1.4 Piecewise affine systems......Page 54
2.1.5 Mixed logical dynamical systems......Page 55
2.1.6 Complementarity systems......Page 56
2.1.7 Discretely controlled continuous systems......Page 57
2.1.9 Hybrid inclusions......Page 58
2.2.2 Modeling power versus decisive power......Page 59
2.3.1 Inadequacy of mono-disciplinary approaches......Page 60
2.3.2 Instability of hybrid systems resulting from switching......Page 61
2.3.3 Zeno behavior......Page 63
2.3.4 Chattering or infinitely fast switching: sliding modes......Page 65
2.3.5 Sensitivity and nondeterminism of the system behavior......Page 66
2.4.1 Necessity for a novel theory on hybrid dynamical systems......Page 67
2.4.2 Solution concepts and well-posedness......Page 68
2.4.4 Control design......Page 70
2.4.5 Observer design......Page 71
2.4.8 Robust stability......Page 72
Bibliographical notes......Page 73
3 Hybrid automata......Page 75
3.1 Definition......Page 77
3.2.1 Linear hybrid automata......Page 80
3.2.3 Timed automata......Page 81
3.3.1 Problem statement......Page 82
3.3.2 Characterizing reachable space......Page 85
3.3.3 Reachable space computation......Page 87
3.3.4 Uncertainty......Page 89
3.4.1 Stability analysis using gain automata......Page 90
3.4.2 Region stability......Page 91
3.4.4 LaSalle's invariance principle......Page 92
3.4.6 Stability analysis using formal methods......Page 93
3.5.1 Control problem......Page 95
3.5.2 The classical Pontryagin's Maximum Principle......Page 96
3.5.3 Extension to a hybrid maximum principle......Page 98
Bibliographical notes......Page 103
4 Switched and piecewise affine systems......Page 105
4.1 Definition of the system class......Page 107
4.2.1 Identification problem......Page 110
4.2.2 Models in input/output form......Page 111
4.2.3 Hybrid system identification problems......Page 112
4.2.4 Data classification and region estimation......Page 115
4.2.5 Four procedures for the identification of SARX/PWARX models......Page 117
4.2.6 Comparison of the identification procedures......Page 122
4.3.1 Preliminaries and basic definitions......Page 124
4.3.2 Observability of switched systems with arbitrary switching......Page 126
4.3.3 Observability of switched systems with minimum dwell time......Page 128
4.4.1 Stability problems......Page 130
4.4.2 Stability notions......Page 131
4.4.3 Stability of differential inclusions......Page 133
4.4.4 Stability analysis of switched linear systems by means of a common Lyapunov function......Page 134
4.4.5 Lie-algebraic stability criteria......Page 136
4.4.7 Multiple Lyapunov functions......Page 137
4.4.8 Stability of discrete-time systems......Page 139
4.5.2 State-space restrictions......Page 142
4.5.3 Time domain restrictions......Page 144
4.5.4 Control design for arbitrary switching......Page 146
4.5.5 Stabilization of discrete-time switched linear systems......Page 147
4.6.1 Decidability and NP-hardness......Page 148
4.6.2 Switched systems and the joint spectral radius......Page 149
4.6.3 Piecewise affine systems......Page 152
Bibliographical notes......Page 154
5 Further switched systems......Page 157
5.1.1 Linear model-predictive control......Page 159
5.1.2 Discrete hybrid automata......Page 161
5.1.3 Mixed logical dynamical systems......Page 163
5.1.4 Hybrid model-predictive control......Page 166
5.2.1 Modeling aim......Page 169
5.2.2 Definition......Page 170
5.2.3 Examples......Page 171
5.2.4 Preliminaries......Page 177
5.2.5 Existence and uniqueness of solutions......Page 179
5.3.1 Summary of the five classes of hybrid models......Page 185
MLD and LC systems......Page 187
PWA and MLD systems......Page 188
MLD and ELC systems......Page 189
5.4.1 Problem statement......Page 191
5.4.2 Model classes......Page 192
5.4.3 Solution concepts......Page 193
5.4.4 Well-posedness notions......Page 196
5.4.5 Comparison of some solution concepts......Page 207
5.4.6 Zenoness......Page 209
Bibliographical notes......Page 210
6 Hybrid systems: quantization and abstraction......Page 211
6.1 Quantization and model abstraction......Page 213
6.2.1 Systems with quantized feedback......Page 214
6.2.2 Issues on the stabilization problem for quantized systems......Page 217
6.2.3 Control under communication constraints......Page 221
6.2.4 Control with quantized sensors and actuators......Page 228
6.2.5 Channel sharing for systems with input constraints......Page 230
6.3.1 Diagnostic problem......Page 231
6.3.2 Hybrid model of quantized systems......Page 232
6.3.3 Properties of quantized systems......Page 233
6.3.4 Discrete-event modeling of quantized systems......Page 236
6.3.5 Diagnosis of quantized systems......Page 238
6.3.6 Example: Diagnosis of the air path of a diesel engine......Page 239
6.4.1 Motivation of abstraction-based design......Page 241
6.4.2 Control problem......Page 242
6.4.3 Behaviors......Page 243
6.4.4 Supervisory control......Page 244
6.4.5 Abstraction-based supervisory control......Page 246
6.4.6 Extensions......Page 248
6.5.1 Stabilization problem for discretely controlled continuous systems......Page 249
6.5.2 Modeling the behavior of discretely controlled continuous systems......Page 252
6.5.3 Stabilization of periodic stationary solutions......Page 256
6.5.4 Application: Event generator design of a boost converter......Page 262
Bibliographical notes......Page 265
7 Stochastic hybrid systems......Page 267
7.1.1 Deterministic and nondeterministic models......Page 268
7.1.2 Hybrid automata......Page 269
7.1.3 Executions......Page 270
7.2.1 Stochastic hybrid automata......Page 273
7.2.2 Special cases and systems with inputs......Page 277
7.3 Discrete-time stochastic hybrid systems......Page 279
7.4.1 Reachability problem......Page 282
7.4.2 Probabilistic safety analysis of stochastic finite automata......Page 283
7.4.3 Probabilistic safety analysis of stochastic hybrid systems......Page 286
7.4.4 Extensions......Page 292
Bibliographical notes......Page 293
Part II Tools......Page 295
8 Overview of tools development and open problems......Page 297
8.1 Control of switched linear systems......Page 298
8.3 Modeling, simulation, and optimization of general hybrid systems......Page 299
8.4 Model transformation......Page 300
8.5 Concluding remarks and open issues......Page 301
9 Verification tools for linear hybrid automata......Page 303
9.1 Formal verification and linear hybrid automata......Page 304
9.2 Modeling systems using linear hybrid automata......Page 305
9.3 Run semantics and path constraints......Page 306
9.4 Reachability analysis......Page 307
9.4.1 Polyhedral computations......Page 308
9.4.2 Over-approximating polyhedra......Page 309
9.5 Over-approximation of affine dynamics......Page 312
Bibliographical notes......Page 313
10 Tools for modeling, simulation, control, and verification of piecewise affine systems......Page 315
10.1.1 Modeling aim......Page 317
10.1.2 The HYSDEL language......Page 318
10.1.3 HYSDEL 3.0 enhancements......Page 319
10.2.1 Functionality of the toolbox......Page 321
10.2.3 Control of constrained systems......Page 323
10.2.4 Analysis of hybrid systems......Page 324
10.2.6 Summary......Page 325
10.3.1 Toolbox features......Page 326
10.3.2 Verification of safety properties......Page 329
10.3.4 Explicit hybrid model-predictive control......Page 331
10.3.5 Applications......Page 332
10.4.1 Hybrid Identification Toolbox......Page 334
10.4.2 Piecewise Affine System Identification Toolbox......Page 335
10.5.1 Interchange architecture......Page 338
10.5.2 Platform-independent format for dt-PWA systems......Page 340
10.5.3 XML scheme of the platform-independent format for PWA systems......Page 341
10.5.4 Implementation of the architecture-specific format in MATLAB......Page 342
11 Modeling, simulation, and optimization environments......Page 343
11.1 Introduction and overview......Page 344
11.2.2 Numerical simulation of hybrid systems......Page 347
11.2.3 MATLAB, Simulink, Stateflow, and SimEvents......Page 350
11.2.4 gPROMS......Page 356
11.2.5 Other tools and environments......Page 364
11.3.1 Optimization problem......Page 368
11.3.2 Numerical optimization of nonlinear hybrid systems......Page 369
11.3.3 Tools for the optimization of nonlinear hybrid systems......Page 371
Bibliographical notes......Page 375
12 Interchange formats and tool integration......Page 379
12.1 Overview of interchange formats for hybrid systems......Page 380
12.2.2 Discrete, continuous, and algebraic variables......Page 383
12.2.3 Urgency......Page 384
12.2.4 Closed and open scopes......Page 386
12.2.5 Input and output variables......Page 387
12.3 Example: Bottle filling system......Page 388
Part III Applications......Page 393
13 Energy management......Page 395
13.1 Introduction to energy management......Page 396
13.2.2 System description and control model derivation......Page 397
13.2.4 Explicit model-predictive control......Page 399
13.2.5 Sampled data control for robust tracking......Page 402
13.2.6 Relaxed dynamical programming......Page 404
13.2.7 Stabilizing control approach......Page 406
Circuit parameters......Page 408
13.3.1 Control problem......Page 411
13.3.2 Power network system......Page 412
13.3.4 Model-predictive control......Page 415
Scenarios......Page 419
13.3.6 Conclusions and future research......Page 420
13.4 Summary and outlook......Page 421
Acknowledgment......Page 422
14 Industrial controls......Page 423
14.1 Introduction to process control applications......Page 424
14.2.1 The evaporator system......Page 425
14.2.2 Task of safety analysis......Page 426
14.2.3 Safety analysis using optimization-based state-space exploration......Page 427
14.2.4 A semi-analytical approach to safety analysis......Page 428
14.2.5 Evaluation of the results......Page 430
14.3.1 Hierarchical abstraction-based control......Page 431
14.3.2 Hierarchical control architecture......Page 432
14.3.3 Bottom-up design procedure......Page 435
14.3.4 Discontinuously operated multiproduct batch plant......Page 437
14.3.5 Hierarchical control of multiproduct batch plant......Page 439
14.4.2 Control of a supermarket refrigeration system......Page 443
14.4.3 Start-up of a multiple-effect evaporator system......Page 448
14.5 Summary and outlook on further industrial control applications......Page 453
15 Automotive control......Page 457
15.1 Introduction......Page 458
15.2.1 System integration......Page 459
15.2.2 Design scenario and design flow......Page 460
15.2.3 Control system design......Page 463
15.3.1 Motivation......Page 470
15.3.2 Survey of MPC applications in vehicle dynamics control......Page 471
15.3.3 Survey of MPC applications in powertrain control......Page 472
15.3.4 Example: Hybrid MPC of magnetic actuators......Page 473
15.4.1 HCCI engine concept......Page 479
15.4.2 Control of ignition timing......Page 481
15.4.3 Properties and model of the HCCI engine......Page 482
Bibliographical notes......Page 487
16 Networked control......Page 489
16.1 Introduction to distributed control applications and networked control systems......Page 490
16.2.1 Coordination of multi-agents system......Page 492
16.2.2 Consensus problems for teams of mobile agents......Page 498
16.2.3 Distributed Kalman filtering using weighted averaging......Page 502
16.3.1 Networked control systems: hybrid modeling issues......Page 505
16.3.2 Controller synthesis......Page 507
16.3.3 Modeling of adaptive transmission behaviors in control over wireless......Page 508
16.3.4 Safety problem with wireless networks and the hybrid model......Page 509
16.4.1 Description of the mining ventilation process......Page 513
16.4.2 Today's control architecture......Page 514
16.4.3 Proposed wireless control architecture......Page 515
16.5 Conclusions and open problems......Page 517
17 Solar air conditioning – a benchmark for hybrid systems control......Page 519
17.1.1 Main components......Page 520
17.1.3 Operating modes of the process......Page 522
17.2 Plant model......Page 523
17.3.1 Control objectives......Page 524
17.3.2 Hybrid control algorithm......Page 525
17.3.3 Experimental results and discussion......Page 526
Bibliographical notes......Page 527
References......Page 529
Index......Page 571