Efficient Modeling and Control of Large-Scale Systems (eBook)

Foreword 6
Preface 8
Contents 12
List of Contributors 18
Part I Model Reduction, Large-Scale System Modelingand Applications 22
Interpolatory Model Reduction of Large-Scale Dynamical Systems 23
1 Introduction 23
2 Problem Setting 24
2.1 The General Interpolation Framework 26
2.2 Model Reduction via Projection 28
2.3 Interpolatory Projections 30
2.4 Error Measures 34
3 Interpolatory Optimal H2 Approximation 38
3.1 An Algorithm for Interpolatory Optimal H2 Model Reduction 41
3.2 Numerical Results for IRKA 42
4 Interpolatory Passivity Preserving Model Reduction 45
4.1 An Example of Passivity Preserving Model Reduction 47
5 Structure-Preserving Model Reduction Using Generalized Coprime Factorizations 50
5.1 A Numerical Example: Driven Cavity Flow 53
5.2 Second-Order Dynamical Systems 55
6 Model Reduction of Parametric Systems 57
6.1 Numerical Example 60
7 Model Reduction from Measurements 61
7.1 Motivation: S-Parameters 61
7.2 The Loewner Matrix Pair and Constructionof Interpolants 62
7.2.1 The General Case 66
7.3 Loewner and Pick Matrices 66
7.4 Examples 67
7.4.1 A Simple Low-order Example 67
7.4.2 Coupled Mechanical System 69
7.4.3 Four-pole Band-pass Filter 72
8 Conclusions 73
References 73
Efficient Model Reduction for the Control of Large-Scale Systems 79
1 Introduction 79
2 Spectral Decomposition 80
3 Simultaneous Gradient Error Reduction 82
4 Balancing 84
4.1 Techniques Not Requiring Balancing 86
4.2 Balancing Over A Disk 88
5 Example: Large-Scale System Application 89
References 91
Dynamics of Tensegrity Systems 93
1 Introduction and Motivation 93
2 Dynamics of a Single Rigid Rod 94
2.1 Nodes as Functions of the Configuration 96
2.2 String Forces 97
2.3 Generalized Forces and Torques 98
2.4 Equations of Motion 98
3 Class 1 Tensegrity Systems 99
4 Class k Tensegrity Systems 102
4.1 A Class 2 Tensegrity Cable Model 102
5 Concluding Remarks 107
References 107
Modeling a Complex Aero-Engine Using Reduced Order Models 109
1 Introduction 109
2 Gas Turbine System 110
2.1 Nonlinear Static Model of Gas Turbine 111
2.2 Nonlinear Dynamic Model of Gas Turbine 112
3 Problem Formulation for Reduced Order Data Driven Modeling 113
3.1 Criterion Selection 114
3.2 Model Selection: EE vs. OE 116
3.2.1 Equation Error (EE) Model 117
3.2.2 Output Error (OE) Model 118
4 NLS for OE Parameter Identification 119
4.1 Calculation of bold0mu mumu equation V(k)/ and the Jacobian 120
4.2 Approximation of R(k) and the Hessian 121
5 Application and Results 124
5.1 First-Order Model 125
5.2 Second-Order Model 129
6 Summary 130
References 130
Part II Large-Scale Systems Control and Applications 132
Robust Control of Large-Scale Systems: Efficient Selection of Inputs and Outputs 133
1 Introduction 133
2 Preliminaries and Problem Formulation 135
2.1 Background on Sum-of-Squares 136
3 Robust Controllability Degree 137
3.1 Special Case: A Polytopic Region 142
3.2 Comparison with Existing Results 146
4 Numerical Example 147
5 Summary 150
References 150
Decentralized Output-Feedback Control of Large-Scale Interconnected Systems via Dynamic High-Gain Scaling 153
1 Introduction 153
2 Decentralized Control Based on The Adaptive Dual Dynamic High-Gain Scaling Paradigm 155
2.1 Assumptions 155
2.2 Observer and Controller Designs 158
2.3 Stability Analysis 159
3 Generalized Scaling: Application to Decentralized Control 169
3.1 Assumptions 170
3.2 Observer Design 172
3.3 Controller Design 173
3.4 Stability Analysis 176
References 182
Decentralized Output Feedback Guaranteed Cost Control of Uncertain Markovian Jump Large-Scale Systems: Local Mode Dependent Control Approach 184
1 Introduction 184
2 Problem Formulation 187
3 Guaranteed Cost Controller Design 190
3.1 Design Methodology 190
3.2 Design of Global Mode Dependent Controllers 193
3.3 The Main Result: Design of Local Mode Dependent Controllers 197
3.4 Design Procedure 199
4 An Illustrative Example 200
5 Conclusions 203
Appendix 1 204
Appendix 2 211
References 212
Consensus Based Multi-Agent Control Algorithms 214
1 Introduction 214
2 Problem Formulation 216
3 Consensus at the Control Input Level 217
3.1 Algorithms Derived from the Local Dynamic Output Feedback Control Laws 217
3.2 Algorithms Derived from the Local Static Feedback Control Laws 222
4 Consensus at the State Estimation Level 224
5 Consensus Based Decentralized Control of UAV Formations 227
5.1 Formation Model 227
5.2 Global LQ Optimal State Feedback 229
5.3 Decentralized State Estimation 230
5.4 Experiments 232
References 234
Graph-Theoretic Methods for Networked Dynamic Systems: Heterogeneity and H2 Performance 236
1 Introduction 236
1.1 Preliminaries and Notations 238
2 Canonical Models of Networked Dynamic Systems 241
3 Analysis and Graph-Theoretic Performance Bounds 246
3.1 Observability and Controllability of NDS 246
3.2 Graph-Theoretic Bounds on NDS Performance 249
4 Topology Design for NDS 258
4.1 H2 Topology Design for NDS Coupled at the Output 259
4.2 Sensor Placement with H2 Performance for NDS Coupled at the State 261
5 Concluding Remarks 263
References 264
A Novel Coordination Strategy for Multi-Agent Control Using Overlapping Subnetworks with Application to Power Systems 267
1 Introduction 267
1.1 Multi-Agent Control of Power Networks 268
1.2 Control of Subnetworks 269
1.3 Optimal Power Flow Control 271
1.4 Goal and Outline of This Chapter 272
2 Modeling of Network Characteristics and Control Objectives 272
2.1 Network Characteristics 272
2.2 Control Objectives 273
2.3 Definition of Subnetworks 273
3 Multi-Agent Control of Touching Subnetworks 274
3.1 Internal and External Nodes 274
3.2 Control Problem Formulation for One Agent 275
3.2.1 Prediction Model 276
3.2.2 Objectives 277
3.3 Control Scheme for Multiple Agents 278
4 Multi-Agent Control for Overlapping Subnetworks 279
4.1 Common Nodes 279
4.2 Control Problem Formulation for One Agent 280
4.2.1 Prediction Model 281
4.2.2 Objectives 282
4.3 Control Scheme for Multiple Agents 283
5 Application: Optimal Flow Control in Power Networks 284
5.1 Parameters of the Power Network 284
5.2 Steady-state Characteristics of Power Networks 284
5.2.1 Transmission Lines 286
5.2.2 Generators 287
5.2.3 Loads 287
5.2.4 FACTS Devices 288
5.2.5 Power Balance 288
5.3 Control Objectives 289
5.4 Setting Up the Control Problems 289
5.5 Simulations 290
5.5.1 Scenario 1: Control of SVCs 290
5.5.2 Scenario 2: Control of TCSCs 291
6 Conclusions and Future Research 293
References 293
Distributed Control Methods for Structured Large-Scale Systems 295
1 Introduction 295
2 Problem Statement 296
2.1 H2 Problem and Exact Solution 297
3 A Rational Laurent Operator Structure Preserving Iterative Approach to Distributed Control 298
3.1 L-Operator Sign Function 300
3.2 Definition 301
3.3 Convergence 301
3.4 Applications 302
3.5 Numerical Difficulties 303
3.6 Application to the Example Problem 304
4 Distributed Control Design for Decomposable Systems 304
4.1 General Description 305
4.2 Application to the Example Problem 308
4.2.1 Generalization to Infinite Dimensional Systems 308
4.2.2 The Platoon 309
5 Distributed LQR of Identical Systems 310
5.1 Special Properties of LQR for Dynamically Decoupled Systems 311
5.2 Application to the Example Problem 313
6 Numerical Results of the Car Platoon Benchmark Problem 315
7 Conclusions and Open Problems 317
References 318
Integrated Design of Large-Scale Collocated Structural System and Control Parameters Using a Norm Upper Bound Approach 320
1 Introduction 320
2 Symmetric Output Feedback Control of Collocated Systems 322
3 Upper Bounds on Collocated Structural System Norms 323
4 Integrated Damping and Control Design Using the Analytical Bound Approach 326
4.1 Integrated Design Based on an H Specification 326
4.2 Integrated Design Based on an H2 Specification 327
4.3 Integrated Design Based on a Mixed H2/H Specification 329
4.4 Decentralized Control Using the Norm Upper Bound Formulation 330
4.5 Additional Remarks 332
5 Simulation Results 332
6 Concluding Remarks 341
References 341
Index 344