Resilient Control of Uncertain Dynamical Systems

✍ Scribed by Magdi S. Mahmoud

• Publisher: Springer
• Year: 2004
• Tongue: English
• Leaves: 272
• Series: Lecture Notes in Control and Information Sciences
• Edition: 1
• Category: Library

✦ Synopsis

This monograph provides a complete description of resilient control theory. It unifies the methods for developing resilient controllers and filters for a class of uncertain dynamical systems and reports recent advances in design methodologies. The book presents an introductory and comprehensive treatment of resilient controller design methods placing great emphasis on the derivation of necessary and sufficient design conditions and on the use of linear matrix inequalities as a convenient computational tool. The book can be used as a graduate-level textbook in control engineering or applied mathematics as well as a reference for practicing engineers, researchers and students.

✦ Table of Contents

Contents......Page 7
1.1 Overview......Page 13
1.2.1 Introduction......Page 14
1.2.2 Robust Control Problem......Page 15
1.2.4 Parameter Space Design......Page 16
1.3 Motivating Examples......Page 18
1.3.1 Inverted Pendulum on a Cart......Page 19
1.3.2 Flexible Disk Drive......Page 21
1.3.3 Simple Heat Exchanger......Page 25
1.3.4 Stream Water Quality......Page 28
1.4 Approaches to Resilient Control......Page 29
1.4.1 Guaranteed-Cost Approach......Page 30
1.4.3 Controller Gain Perturbations......Page 31
1.4.4 Multiplicative Type......Page 32
1.5.1 General Terms......Page 33
1.6 Outline of the Book......Page 34
1.6.2 Chapter Organization......Page 35
1.7 Notes and References......Page 37
2.1 Introduction......Page 39
2.2 Model with Norm-Bounded Uncertainties......Page 40
2.3 Guaranteed Cost Control I......Page 41
2.3.1 Quadratic Stability......Page 42
2.3.2 Additive Gain Perturbations......Page 43
2.3.3 Multiplicative Gain Perturbations......Page 45
2.3.4 Special Cases......Page 46
2.3.5 Example 2.1......Page 48
2.4.1 Additive Gain Perturbations......Page 49
2.4.2 Multiplicative Gain Perturbations......Page 50
2.4.3 Special Cases......Page 51
2.5 Dynamic Feedback Control I......Page 53
2.5.1 Parameterization......Page 55
2.5.2 Design Procedure......Page 56
2.5.3 Example 2.3......Page 58
2.6 Model with Convex-Polytopic Uncertainties......Page 59
2.7.1 Quadratic Stability......Page 61
2.7.2 Additive Gain Perturbations......Page 63
2.7.3 Multiplicative Gain Perturbations......Page 64
2.7.4 Special Cases......Page 65
2.8 H∞ Control II......Page 67
2.8.1 Additive Gain Perturbations......Page 69
2.8.3 Special Case......Page 70
2.8.4 Results for Delayless Systems......Page 71
2.8.5 Example 2.6......Page 72
2.9 Dynamic Feedback Control II......Page 73
2.9.1 Guaranteed Cost Design......Page 75
2.9.2 H∞ Design......Page 77
2.9.3 Special Cases......Page 79
2.9.4 Example 2.7......Page 81
2.10.1 Resilient Feedback Control......Page 83
2.10.2 Error Dynamics......Page 84
2.10.3 Robust Stability Results......Page 86
2.10.4 Special Cases......Page 89
2.10.6 Example 2.9......Page 93
2.11 Notes and References......Page 94
3.1 Introduction......Page 95
3.2.2 Quadratic Stability......Page 96
3.3.1 Additive Gain Perturbations......Page 98
3.3.2 Multiplicative Gain Perturbations......Page 101
3.3.4 Example 3.2......Page 102
3.4 H∞ Control Synthesis......Page 103
3.5 Design Example......Page 107
3.6 Notes and References......Page 108
4.2 Continuous-Time Model......Page 111
4.2.1 Nominal Model......Page 112
4.3 Adaptive Schemes......Page 113
4.3.1 Known Perturbation Bound......Page 114
4.3.3 Unknown Gain Perturbation Bound......Page 116
4.3.4 Example 4.2......Page 118
4.4 Polytopic Model......Page 120
4.5 Design Results......Page 121
4.5.1 Known Perturbation Bound......Page 122
4.5.2 Example 4.3......Page 123
4.5.3 Unknown Gain Perturbation Bound......Page 124
4.5.5 Model Reference State Regulation......Page 126
4.5.6 Example 4.5......Page 129
4.6 Discrete-Time Model......Page 130
4.6.1 Stability and Stabilization Results......Page 131
4.7.1 Known Perturbation Bound......Page 134
4.7.2 Unknown Perturbation Bound......Page 135
4.8.1 Example 4.6......Page 136
4.8.2 Example 4.7......Page 138
4.9 Notes and References......Page 139
5.1 Introduction......Page 141
5.2 A Class of Uncertain Systems......Page 142
5.3 The Resilient Filter......Page 143
5.3.2 LMI-Based Design Conditions......Page 144
5.3.3 Special Case......Page 146
5.3.4 A Limiting Approach to Kalman Filtering......Page 147
5.3.5 Multiplicative Gain Perturbations......Page 149
5.3.7 Example 5.2......Page 150
5.4 Continuous Polytopic Systems......Page 151
5.5 The Resilient Filtering Problem......Page 152
5.5.1 Stability Results......Page 153
5.5.2 Delay-Independent Filter Synthesis......Page 155
5.5.3 Multiplicative Gain Perturbations......Page 158
5.6.1 A Descriptor Approach......Page 161
5.6.2 Extended Newton-Leibniz Approach......Page 166
5.7.1 Example 5.3......Page 173
5.7.2 Example 5.4......Page 176
5.7.3 Example 5.5......Page 177
5.7.4 Example 5.6......Page 178
5.7.5 Example 5.7......Page 179
5.8 Notes and References......Page 181
6.1 Introduction......Page 183
6.2.1 Descriptor Transformation......Page 184
6.3.1 Nominal H2 Design......Page 185
6.3.2 Resilient H2 Design......Page 188
6.3.3 Nominal H∞ Design......Page 190
6.3.5 Simultaneous Nominal H2/H∞ Design......Page 192
6.3.6 Simultaneous Resilient H2/H∞ Design......Page 193
6.3.8 Example 6.2......Page 194
6.3.9 Example 6.3......Page 195
6.4 Continuous Polytopic Systems......Page 196
6.4.1 Polytopic H2 Design......Page 197
6.4.2 Polytopic H∞ Design......Page 198
6.4.3 Simultaneous Polytopic H2/H∞ Design......Page 199
6.5.1 System Description......Page 200
6.5.2 Descriptor Model Transformation......Page 201
6.5.3 Robust Stability......Page 206
6.5.4 Nominal Feedback Stabilization......Page 207
6.5.5 Resilient Feedback Stabilization......Page 211
6.5.8 Example 6.7......Page 213
6.5.9 Time-Varying Delay-Dependent Stability......Page 214
6.5.10 Example 6.8......Page 216
6.6 Notes and References......Page 217
7.2 Nonlinear Continuous-Time Systems......Page 219
7.3.1 Robust Delay-Independent Stability......Page 220
7.3.2 Example 7.1......Page 222
7.3.3 Robust Delay-Dependent Stability......Page 223
7.3.4 Example 7.2......Page 227
7.4.1 Nominal Feedback Design......Page 228
7.4.2 Example 7.3......Page 229
7.4.4 Resilient Feedback Design......Page 231
7.4.5 Example 7.5......Page 234
7.5 Nonlinear Discrete-Time Systems......Page 235
7.6 Robust Stability......Page 236
7.7 Robust Stabilization......Page 239
7.7.2 Example 7.9......Page 241
7.7.4 Resilient Feedback Design......Page 243
7.7.5 Example 7.11......Page 246
7.8 Notes and References......Page 247
8.1.2 Inequality 2......Page 249
8.1.4 Inequality 4 (Schur Complements)......Page 250
8.2 Lemmas......Page 252
8.3.1 Basics......Page 255
8.3.2 Some Standard Problems......Page 257
8.3.3 The S-Procedure......Page 258
8.5.1 Inverse of Block Matrices......Page 259
8.5.2 Matrix Inversion Lemma......Page 260
About the Author......Page 261
References......Page 263
Index......Page 269