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Variance-Constrained Multi-Objective Stochastic Control and Filtering

Variance-Constrained Multi-Objective Stochastic Control and Filtering

Lifeng Ma, Zidong Wang, Yuming Bo

ISBN: 978-1-118-92949-0

Jun 2015

336 pages

In Stock

$150.00

Description

  • Unifies existing and emerging concepts concerning multi-objective control and stochastic control with engineering-oriented phenomena
  • Establishes a unified theoretical framework for control and filtering problems for a class of discrete-time nonlinear stochastic systems with consideration to performance
  • Includes case studies of several nonlinear stochastic systems
  • Investigates the phenomena of incomplete information, including missing/degraded measurements, actuator failures and sensor saturations
  • Considers both time-invariant systems and time-varying systems
  • Exploits newly developed techniques to handle the emerging mathematical and computational challenges

Preface vii

Acknowledgements ix

List of Abbreviations xi

1 Introduction 1

1.1 Analysis and Synthesis of Nonlinear Stochastic Systems 2

1.1.1 Nonlinear Systems 3

1.1.2 Stochastic Systems 4

1.2 Multi-Objective Control and Filtering with Variance Constraints 5

1.2.1 Covariance Control Theory 5

1.2.2 Multiple Performance Requirements 7

1.2.3 Design Techniques for Nonlinear Stochastic Systems with Variance Constraints 9

1.2.4 A Special Case of Multi-Objective Design: Mixed H2/H1 Control/Filtering 11

1.3 Outline 12

2 Robust H1 Control with Variance Constraints 17

2.1 Problem Formulation 18

2.2 Stability, H1 Performance and Variance Analysis 20

2.2.1 Stability, H1 Performance Analysis 21

2.2.2 Variance Analysis 23

2.3 Robust Controller Design 27

2.4 Numerical Example 30

2.5 Summary 33

3 Robust Mixed H2=H1 Filtering 41

3.1 System Description and Problem Formulation 42

3.2 Algebraic Characterizations for Robust H2=H1 Filtering 44

3.2.1 Robust H2 Filtering 44

3.2.2 Robust H1 Filtering 50

3.3 Robust H2=H1 Filter Design Techniques 51

3.4 An Illustrative Example 60

3.5 Summary 62

4 Filtering with Missing Measurements 63

4.1 Problem Formulation 64

4.2 Stability and Variance Analysis 67

4.3 Robust Filter Design 71

4.4 Numerical Example 75

4.5 Summary 78

5 Robust Fault-Tolerant Control 87

5.1 Problem Formulation 88

5.2 Stability and Variance Analysis 90

5.3 Robust Controller Design 92

5.4 Numerical Example 98

5.5 Summary 103

6 Robust H2 SMC 105

6.1 The System Model 106

6.2 Robust H2 Sliding Mode Control 107

6.2.1 Switching Surface 107

6.2.2 Performances of the Sliding Motion 108

6.2.3 Computational Algorithm 114

6.3 Sliding Mode Controller 115

6.4 Numerical Example 116

6.5 Summary 118

7 Dissipative Control with Degraded Measurements 125

7.1 Problem Formulation 126

7.2 Stability, Dissipativity and Variance Analysis 129

7.3 Observer-Based Controller Design 134

7.3.1 Solvability of Multi-Objective Control Problem 134

7.3.2 Computational Algorithm 139

7.4 Numerical Example 140

7.5 Summary 142

8 Variance-Constrained H1 Control with Multiplicative Noises 145

8.1 Problem Formulation 146

8.2 Stability, H1 Performance, Variance Analysis 147

8.2.1 Stability 148

8.2.2 H1 performance 150

8.2.3 Variance analysis 152

8.3 Robust State Feedback Controller Design 153

8.4 A Numerical Example 156

8.5 Summary 157

9 Robust Finite-Horizon H1 Control 159

9.1 Problem Formulation 160

9.2 Performance Analysis 162

9.2.1 H1 Performance 162

9.2.2 Variance Analysis 164

9.3 Robust Finite Horizon Controller Design 167

9.4 Numerical Example 171

9.5 Summary 173

10 Finite-Horizon Filtering with Degraded Measurements 177

10.1 Problem Formulation 178

10.2 Performance Analysis 181

10.2.1 H1 Performance Analysis 181

10.2.2 System Covariance Analysis 186

10.3 Robust Filter Design 187

10.4 Numerical Example 190

10.5 Summary 191

11 Mixed H2=H1 Control with Randomly Occurring Nonlinearities: the Finite-Horizon Case 197

11.1 Problem Formulation 199

11.2 H1 Performance 200

11.3 Mixed H2=H1 Controller Design 204

11.3.1 State-Feedback Controller Design 204

11.3.2 Computational Algorithm 207

11.4 Numerical Example 207

11.5 Summary 211

12 Finite-Horizon H2=H1 Control of MJSs with Sensor Failures 213

12.1 Problem Formulation 214

12.2 H1 Performance 216

12.3 Mixed H2=H1 Controller Design 220

12.3.1 Controller Design 220

12.3.2 Computational Algorithm 224

12.4 Numerical Example 224

12.5 Summary 227

13 Finite-Horizon Control with ROSF 229

13.1 Problem Formulation 230

13.2 H1 And Covariance Performances Analysis 234

13.2.1 H1 Performance 234

13.2.2 Covariance Analysis 238

13.3 Robust Finite-Horizon Controller Design 240

13.3.1 Controller Design 240

13.3.2 Computational Algorithm 243

13.4 Numerical Example 243

13.5 Summary 244

14 Finite-Horizon H2=H1 Control with Actuator Failures 247

14.1 Problem Formulation 248

14.2 H1 Performance 251

14.3 Multi-Objective Controller Design 253

14.3.1 Controller Design 253

14.3.2 Computational Algorithm 256

14.4 Numerical Example 257

14.5 Summary 259

15 Conclusions and Future Topics 261

References 263