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Chapter 1 Data-Rate Theorem for Networked Control Systems 1
1��1 Linear Discrete-Time Systems 1
1��1��1 Introduction 1
1��1��2 Problem Formulation 4
1��1��3 State Estimation under Data-Rate Limitations 5
1��1��4 Numerical Examples and Simulations 19
1��2 Linear Continuous Time-Invariant Systems 21
1��2��1 Introduction 22
1��2��2 Problem Formulation 23
1��2��3 State Estimation under Information Limitations 24
1��2��4 Numerical Examples and Simulations 26
References 28
Chapter 2 Coding Schemes for Observability and Stabilizability under
Data-Rate Limitations 31
2��1 Variable-Length Coding 31
2��1��1 Introduction 31
2��1��2 Problem Formulation 33
2��1��3 Quantization�� Coding and Control Schemes 35
2��1��4 Sufficient Conditions for Observability and Stabilizability 40
2��1��5 Numerical Examples and Simulations 50
2��2 Fixed-Length Coding 53
2��2��1 Introduction 53
2��2��2 Problem Formulation 54
2��2��3 Quantization and Coding 55
2��2��4 Numerical Examples and Simulations 61
2��3 Time-Varying Coding 62
2��3��1 Introduction 63
2��3��2 Problem Formulation 64
2��3��3 Quantization and Coding 65
2��3��4 Numerical Examples and Simulations 72
References 74
Chapter 3 State Estimation under Data-Rate Limitations 78
3��1 Scalar Linear Continuous Time-Invariant Systems 78
3��1��1 Introduction 78
3��1��2 Problem Formulation 79
3��1��3 Conditions on the Constant Data Rate for Observability 80
3��1��4 Numerical Examples and Simulations 83
3��2 Multi-Input Multi-Output Linear Systems 85
3��2��1 Introduction 85
3��2��2 Problem Formulation 86
3��2��3 Conditions on the Constant Data Rate for Observability 88
3��2��4 Numerical Examples and Simulations 91
3��3 Jordan Canonical Form of System Matrix 93
3��3��1 Introduction 93
3��3��2 Problem Formulation 94
3��3��3 A Lower Bound on the Data Rate for Observability 96
3��4 Linear Discrete-Time Systems with Extreme Data-Rate Limitations 100
3��4��1 Introduction 100
3��4��2 Problem Formulation 101
3��4��3 Optimal Encoder and Decoder Design 102
3��4��4 Numerical Examples and Simulations 105
3��5 Linear Continuous-Time Systems with Extreme Data-Rate Limitations 106
3��5��1 Introduction 107
3��5��2 Problem Formulation 108
3��5��3 Conditions for Observability 109
3��5��4 Numerical Examples and Simulations 112
References 113
Chapter 4 Observability and Stabilizability of Linear Systems with Time
Delays 117
4��1 Systems with Random Time Delays 117
4��1��1 Introduction 117
4��1��2 Problem Formulation 119
4��1��3 State Estimation over Channels with Random Time Delays 120
4��1��4 Numerical Examples and Simulations 124
4��2 Systems with Random Time Delays and Limited Data-Rates 126
4��2��1 Introduction 126
4��2��2 Problem Formulation 127
4��2��3 Optimal Encoder and Decoder Design 130
4��2��4 Conditions for Observability 132
4��2��5 Numerical Examples and Simulations 142
4��3 Systems with Fixed Time Delay 146
4��3��1 Introduction 146
4��3��2 Problem Formulation 147
4��3��3 Control under Communication Constraints 148
4��3��4 Numerical Examples and Simulations 152
References 154
Chapter 5 State Estimation over Limited Capacity and Dropout Channels 158
5��1 Observability over an AWGN Channel 158
5��1��1 Introduction 158
5��1��2 Problem Formulation 159
5��1��3 State Estimation over AWGN Channels 160
5��1��4 Numerical Examples and Simulations 163
5��2 Observability under Packet Dropout and Time Delay 165
5��2��1 Introduction 165
5��2��2 Problem Formulation 166
5��2��3 Sufficient Conditions for Observability 167
5��2��4 Numerical Examples and Simulations 170
References 173
Chapter 6 Linear Quadratic Control for Networked Control Systems with
Information Limitations 176
6��1 LQ Cost for Plant States 176
6��1��1 Introduction 176
6��1��2 Problem Formulation 177
6��1��3 LQ Control under Information Limitations 178
6��2 LQ Cost for Plant States and Control Inputs 184
6��2��1 Introduction 184
6��2��2 Problem Formulation 186
6��2��3 Control Scheme under Information Rate Limitations 186
6��2��4 Numerical Examples and Simulations 190
References 192