Front Cover

Estimation and Control of Large-Scale Networked Systems

Copyright

Contents

Preface

Acknowledgments

Notation and Symbols

1 Introduction

1.1 A General View on Control System Design

1.2 Communication and Control

1.3 Book Contents

1.3.1 Controllability and Observability of a Control System

1.3.2 Centralized and Distributed State Estimations

1.3.3 State Estimations and Control With Imperfect Communications

1.3.4 Verification of Stability and Robust Stability

1.3.5 Distributed Controller Design for an LSS

1.3.6 Structure Identification for an LSS

1.3.7 Attack Estimation/Identification and Other Issues

1.4 Bibliographic Notes

References

2 Background Mathematical Results

2.1 Linear Space and Linear Algebra

2.1.1 Vector and Matrix Norms

2.1.2 Hamiltonian Matrices and Distance Among Positive Definite Matrices

2.2 Generalized Inverse of a Matrix

2.3 Some Useful Transformations

2.4 Set Function and Submodularity

2.5 Probability and Random Process

2.6 Markov Process and Semi-Markov Process

2.7 Bibliographic Notes

References

3 Controllability and Observability of an LSS

3.1 Introduction

3.2 Controllability and Observability of an LTI System

3.2.1 Minimal Number of Inputs/Outputs Guaranteeing Controllability/Observability

3.2.2 A Parameterization of Desirable Input/Output Matrices

3.2.3 Some Nitpicking

3.3 A General Model for an LSS

3.4 Controllability and Observability for an LSS

3.4.1 Subsystem Transmission Zeros and Observability of an LSS

3.4.2 Observability Verification

3.4.3 A Condition for Controllability and Its Verification

3.4.4 In/Out-degree and Controllability/Observability of a Networked System

3.5 Construction of Controllable/Observable Networked Systems

3.6 Bibliographic Notes

Appendix 3.A

3.A.1 Proof of Theorem 3.4

3.A.2 Proof of Theorem 3.8

3.A.3 Proof of Theorem 3.9

3.A.4 Proof of Theorem 3.10

References

4 Kalman Filtering and Robust Estimation

4.1 Introduction

4.2 State Estimation and Observer Design

4.3 Kalman Filter as a Maximum Likelihood Estimator

4.3.1 Derivation of the Kalman Filter

4.3.2 Convergence Property of the Kalman Filter

4.4 Recursive Robust State Estimation Through Sensitivity Penalization

4.4.1 Estimation Algorithm

4.4.2 Derivation of the Robust Estimator

4.4.3 Asymptotic Properties of the Robust State Estimator

4.4.4 Boundedness of Estimation Errors

4.5 Bibliographic Notes

Appendix 4.A

4.A.1 Proof of Theorem 4.1

4.A.2 Proof of Theorem 4.3

References

5 State Estimation With Random Data Droppings

5.1 Introduction

5.2 Intermittent Kalman Filtering (IKF)

5.2.1 The IKF Algorithm

5.2.2 Mean Square Stability of the IKF

5.2.3 Weak Convergence of the IKF

5.3 IKF With Switching Sensors

5.3.1 Mean Square Stability

5.3.2 Second-Order Systems

5.3.3 Extension to Higher-Order Systems

5.4 IKF With Coded Measurement Transmission

5.4.1 Linear Temporal Coding

5.4.2 The MMSE Filter

5.4.3 Mean Square Stability

5.5 Robust State Estimation With Random Data Droppings

5.5.1 System With Parametric Errors

5.5.2 Robust State Estimator

5.5.3 Convergence of the Robust State Estimator

5.6 Asymptotic Properties of State Estimations With Random Data Dropping

5.6.1 Unified Problem Description and Preliminaries

5.6.2 Asymptotic Properties of the Random Matrix Recursion

5.6.3 Approximation of the Stationary Distribution

5.7 Bibliographic Notes

Appendix 5.A

5.A.1 Proof of Theorem 5.18

5.A.2 Proof of Theorem 5.19

5.A.3 Proof of Lemma 5.11

5.A.4 Proof of Theorem 5.20

5.A.5 Proof of Theorem 5.21

5.A.6 Proof of Theorem 5.22

References

6 Distributed State Estimation in an LSS

6.1 Introduction

6.2 Predictor Design With Local Measurements

6.2.1 Derivation of the Optimal Gain Matrix

6.2.2 Relations With the Kalman Filter

6.2.3 Robustification of the Distributed Predictor

6.3 Distributed State Filtering

6.4 Asymptotic Property of the Distributed Observers

6.5 Distributed State Estimation Through Neighbor Information Exchanges

6.6 Bibliographic Notes

Appendix 6.A

6.A.1 Proof of Theorem 6.1

6.A.2 Proof of Theorem 6.2

6.A.3 Proof of Theorem 6.3

6.A.4 Proof of Theorem 6.4

6.A.5 Derivation of Eqs. (6.46) and (6.47)

6.A.6 Proof of Theorem 6.7

6.A.7 Proof of Theorem 6.8

References

7 Stability and Robust Stability of a Large-Scale NCS

7.1 Introduction

7.2 A Networked System With Discrete-Time Subsystems

7.2.1 System Description

7.2.2 Stability of a Networked System

7.2.3 Robust Stability of a Networked System

7.3 A Networked System With Continuous-Time Subsystems

7.3.1 Modeling Errors Described by IQCs

7.3.2 Robust Stability With IQC-Described Modeling Errors

7.4 Concluding Remarks

7.5 Bibliographic Notes

Appendix 7.A

7.A.1 Proof of Theorem 7.3

7.A.2 Proof of Theorem 7.4

References

8 Control With Communication Constraints

8.1 Introduction

8.2 Entropies and Capacities of a Communication Channel

8.2.1 Entropy in Information Theory

8.2.2 Topological Entropy in Feedback Theory

8.2.3 Channel Capacities

8.3 Stabilization Over Communication Channel

8.3.1 Classical Approach for Quantized Control

8.4 Universal Lower Bound

8.5 Coder-Decoder Design

8.6 Extension to Lossy Channels

8.6.1 Erasure Channels

8.6.2 Gilbert-Elliott Channels

8.7 Bibliographic Notes

References

9 Distributed Control for Large-Scale NCSs

9.1 Introduction

9.2 Consensus of Multiagent Systems

9.2.1 Communication Graph

9.2.2 Consensus of Multiagent Systems

9.3 Consensus Control With Relative State Feedback

9.3.1 Design of Consensus Gain

9.3.2 Extensions to Digraphs

9.3.3 Performance Analysis

9.3.4 Optimal Consensus Control for Second-Order Systems

9.4 Consensus Control With Relative Output Feedback

9.4.1 Distributed Observer-Based Protocol

9.4.2 Consensus Under Static Protocol

9.4.3 Consensus Under Dynamic Protocol

9.4.4 Multiagent Systems With Double Integrators

9.5 Formation Control for Multiagent Systems

9.5.1 Vehicle Formation With Double Integrators

9.5.2 Formation-Based Tracking Problem

9.6 Simulations and Experiments

9.6.1 Modeling

9.6.2 Simulation Results

9.7 Bibliographic Notes

References

10 Structure Identification for Networked Systems

10.1 Introduction

10.2 Steady-State Data-Based Identification

10.2.1 Description of the Inference Procedure

10.2.2 Identification Algorithm

Position Determination for Direct Regulations

Estimation of Regulation Coefficients

Determination of the Number of Direct Regulations

10.3 Absolute and Relative Variations in GRN Structure Estimations

10.3.1 Maximum Likelihood Estimation for Wild-Type Expression Level and Measurement Error Variance

10.3.2 Estimation of Relative Expression Level Variations

10.3.3 Estimation Algorithm

10.4 Estimation With Time Series Data

10.4.1 Robust Structure Identification Algorithm for GRNs

10.4.2 Convergence Analysis of the Robust Structure Identification Algorithm

10.5 Bibliographic Notes

Appendix 10.A

10.A.1 Proof of Theorem 10.4

10.A.2 Proof of Theorem 10.5

References

11 Attack Identification and Prevention in Networked Systems

11.1 Introduction

11.2 The SCADA System

11.3 Attack Prevention and System Transmission Zeros

11.3.1 Zero Dynamics and Transmission Zeros

11.3.2 Attack Prevention

11.4 Detection of Attacks

11.5 Identification of Attacks

11.6 System Security and Sensor/Actuator Placement

11.6.1 Some Properties of the Kalman Filter

11.6.2 Sensor Placements

11.6.3 Actuator Placements

11.7 Concluding Remarks

11.8 Bibliographic Notes

Appendix 11.A

11.A.1 Proof of Theorem 11.7

References

12 Some Related Issues

12.1 Introduction

12.2 Cooperation Over Communications

12.2.1 Time Synchronization

12.2.2 State Consensus

Fixed Topology Case

Time-Varying Topology Case

12.3 Adaptive Mean-Field Games for Large Population Coupled ARX Systems With Unknown Coupling Strength

Introduction

Problem Formulation

Control Design

Closed-Loop Analysis

12.4 Other Topics and Theoretical Challenges

12.5 Bibliographic Notes

Appendix 12.A

12.A.1 Proof of Theorem 12.5

References

Index

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