Analysis and Design of Nonlinear Control Systems (eBook)

Preface 7
Contents 11
List of Contributors 14
Short Curriculum Vitae of Alberto Isidori 18
Selected publications of Alberto Isidori 19
Books 19
Selected Publications in Archival Journals 19
Part I System Analysis 24
Smooth Distributions Are Globally Finitely Spanned 25
1 Introduction 25
2 Statement and Proof of the Main Result 26
References 30
Uniformly Universal Inputs 31
1 Introduction 31
2 Analytic Input/Output Operators 32
3 Uniformly Universal Inputs 34
4 Proofs of Theorems 1 and 2 36
5 State Space Systems 43
References 45
System Interconnection 47
1 Introduction 47
2 Tearing, Zooming, and Linking 49
3 Behavioral Systems 50
4 Formalization 52
5 Interconnected Behavior 60
6 Conclusions 60
Acknowledgments 61
References 61
Reduced Order Modeling of Nonlinear Control Systems 62
1 Introduction 62
2 Input Normal Form of Degree d 63
3 Linear Model Reduction 72
4 Nonlinear Model Reduction 75
5 Linear Error Estimates 77
6 Nonlinear Error Estimates 78
7 Example 80
8 Conclusion 82
References 83
Part II Optimization Methods 84
Nonholonomic Trajectory Optimization and the Existence of Twisted Matrix Logarithms 85
1 Introduction 85
2 Some Preliminaries 87
3 Some Properties of the Linearization 89
4 Main Theorem 91
5 The Nilpotent Approximation 94
6 Shortest Paths 95
References 96
The Hamilton-Jacobi Type Equations for Nonlinear Target Control and Their Approximation 97
1 Introduction 97
2 Backward Reachability from Moving Target Set 98
3 The Verification Problem for Moving Target Sets 101
4 Linear Systems Ò Approximating Nonconvex Reachability Sets 103
5 Conclusion 108
References 109
Causal Coding of Markov Sources with Continuous Alphabets 111
1 Introduction 111
2 Preliminaries 114
3 Problem Formulation 114
4 The Structure of Optimal Deterministic Quantizers 115
5 The Infinite-Horizon Solution 119
6 The Structure of Optimal Randomized Quantizers 121
7 On Innovation Encoding 123
8 Concluding Remarks 125
9 Acknowledgments 125
A Weak Topology 125
B Markov Decision Processes 126
References 127
Pseudospectral Optimal Control and Its Convergence Theorems 129
1 Introduction 129
2 Problem Definition 131
3 Problems with Continuous Optimal Control 134
4 Problems with Discontinuous Optimal Control 135
5 A Convergence Theorem without Assumptions 1 and 2 137
6 Conclusion 142
References 142
Part III Feedback Design 145
Event Based Control 146
1 Introduction 146
2 Examples 148
3 Comparison of Periodic and Event Based Control 149
4 A General Structure 153
5 An Example 157
6 Conclusions 163
References 163
Zero Dynamics and Tracking Performance Limits in Nonlinear Feedback Systems 167
1 Introduction 167
2 Bode T-Integral and Cheap Control 168
3 Performance Limits in Nonlinear Feedback Systems 170
4 Illustrative Example 173
5 Concluding Remarks 175
References 175
A Nonlinear Model for Combustion Instability: Analysis and Quenching of the Oscillations 178
1 Introduction 178
2 First K-B Approximation for Autonomous Multi- Resonator Systems 181
3 Simple Case Study: Generalized Van der Pol Equation 181
4 Combustion Instability Model 184
5 Quenching the Oscillations 193
6 Conclusion 197
References 197
Convexification of the Range-Only Station Keeping Problem 199
1 Introduction 199
2 Formulation 201
3 Error Models 203
4 Station Keeping Supervisory Controller 205
5 Results 213
6 Definitions for L and S 215
7 Semi-Definite Programming Formulation 218
8 Concluding Remarks 219
Acknowledgments 219
References 219
Control of Hydraulic Devices, an Internal Model Approach 222
1 Introduction 222
2 The Mechanics and Hydraulics 223
3 Design Goals and Methods 226
4 Gap Control of a Four High Stand 230
5 Conclusions 236
References 236
Hybrid Zero Dynamics of Planar Bipedal Walking 237
1 Introduction 237
2 Why Study Underactuation? 238
3 Hybrid Model of a Bipedal Walker 239
4 Feedback Design via Posture Control 242
5 The Zero Dynamics of Walking 243
6 Experimental Data 248
7 Conclusions 250
8 Acknowledgments 250
References 250
Part IV Regulation 252
Hybrid Systems: Limit Sets and Zero Dynamics with a View Toward Output Regulation 253
1 Introduction 253
2 Hybrid Dynamical Systems 254
3 O-Limit Sets 256
4 Pre-Asymptotically Stable Compact Sets 262
5 Minimum Phase Zero Dynamics 264
6 Feedback Stabilization for a Class of Strongly Minimum Phase, Relative Degree One Hybrid Systems 268
7 Comments on Output Regulation and Conclusions 271
References 272
Essential and Redundant Internal Models in Nonlinear Output Regulation 274
1 Introduction 274
2 The Framework of Output Regulation 276
3 Essential and Redundant Internal Models 281
4 Conclusions 289
A A Reduction Result 289
B Proof of Proposition 5 292
References 293
Two Global Regulators for Systems with Measurable Nonlinearities and Unknown Sinusoidal Disturbances 295
1 Introduction 295
2 Problem Statement 298
3 A Regulator for Minimum Phase Systems 298
4 A Regulator for Non-Minimum Phase Systems 301
5 Conclusion 310
References 310
A Taxonomy for Time-Varying Immersions in Periodic Internal- Model Control 313
1 Notation and Background 313
2 Definition of the Problem 314
3 A Taxonomy for Periodic Internal Model Control 317
4 Weak Immersions for Adaptive Robust Regulation 324
5 Conclusions 327
References 327
Paving the Way Towards the Control of Wireless Telecommunication Networks 329
1 Introduction 329
2 Model-Based Control of Communication Networks 334
3 Dynamic Resource Allocation (DRA) Algorithm for Satellite Networks 338
4 Congestion Control for Terrestrial Networks 341
5 Conclusions 345
References 346
Nonlinear Synchronization of Coupled Oscillators: The Polynomial Case 348
1 Introduction 348
2 Preliminaries 349
3 Feedback Synchronization of Coupled Oscillators 350
4 Examples 355
5 Summary and Outlook 359
References 359
Part V Geometric Methods 361
Disturbance Decoupling for Open Quantum Systems: Quantum Internal Model Principle 362
1 Introduction 362
2 Previous Work in the Literature 363
3 Mathematical Preliminaries 364
4 Invariance for the Quantum System 367
5 Feedback Control 368
6 Invariant Subspace Formalism 371
7 Extension to Control Algebra 373
8 Quantum Internal Model Principle 378
9 Classical and Quantum Disturbance Decoupling 379
10 Conclusion 380
References 381
Controller and Observer Normal Forms in Discrete- Time 383
1 Introduction 383
2 Context and Problem Settlement 385
3 Controller Normal Forms 389
4 Observer Normal Forms 395
5 Conclusions 401
References 401
A Geometric Approach to Dynamic Feedback Linearization 403
1 Introduction 403
2 Preliminaries 404
3 The Algorithm 412
4 Some Examples 413
5 Conclusions 416
Acknowledgments 416
References 416
Part VI Asymptotic Analysis 418
The Steady-State Response of a Nonlinear Control System, Lyapunov Stable Attractors, and Forced Oscillations 419
1 Averaging 419
2 Limit Sets 422
3 The Steady State Behavior of a Nonlinear System 425
4 Examples 426
References 431
Model Reduction by Moment Matching for Linear and Nonlinear Systems 432
1 Introduction 432
2 Model Reduction by Moment Matching for Linear Systems Ò Revisited 433
3 Nonlinear Systems 439
4 Summary 445
Acknowledgments 446
References 446
Adaptive Control of Nonlinear Systems with Unknown Parameters by Output Feedback: A Non- Identifier- Based Method 448
1 Introduction 448
2 Proof of the Main Result 451
3 Extension and Discussion 457
4 Conclusion 460
A Proof of Proposition 1 460
References 465
Hybrid Feedback Stabilization of Nonlinear Systems with Quantization Noise and Large Delays 467
1 Introduction 467
2 Preliminaries 469
3 Main Result 472
4 Change of Coordinates 474
5 Analysis 477
6 Conclusion 483
References 483