Variance-Constrained Multi-Objective Stochastic Control and Filtering

Content: 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