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.
Author(s): Magdi S. Mahmoud
Series: Lecture Notes in Control and Information Sciences
Edition: 1
Publisher: Springer
Year: 2004
Language: German
Pages: 265
front-matter.pdf......Page 1
1.1 Overview......Page 12
1.2.1 Introduction......Page 13
1.2.2 Robust Control Problem......Page 14
1.2.4 Parameter Space Design......Page 15
1.3 Motivating Examples......Page 17
1.3.1 Inverted Pendulum on a Cart......Page 18
1.3.2 Flexible Disk Drive......Page 20
1.3.3 Simple Heat Exchanger......Page 24
1.3.4 Stream Water Quality......Page 27
1.4 Approaches to Resilient Control......Page 28
1.4.1 Guaranteed-Cost Approach......Page 29
1.4.3 Controller Gain Perturbations......Page 30
1.4.4 Multiplicative Type......Page 31
1.5.1 General Terms......Page 32
1.6 Outline of the Book......Page 33
1.6.2 Chapter Organization......Page 34
1.7 Notes and References......Page 36
2.1 Introduction......Page 37
2.2 Model with Norm-Bounded Uncertainties......Page 38
2.3 Guaranteed Cost Control I......Page 39
2.3.1 Quadratic Stability......Page 40
2.3.2 Additive Gain Perturbations......Page 41
2.3.3 Multiplicative Gain Perturbations......Page 43
2.3.4 Special Cases......Page 44
2.3.5 Example 2.1......Page 46
2.4.1 Additive Gain Perturbations......Page 47
2.4.2 Multiplicative Gain Perturbations......Page 48
2.4.3 Special Cases......Page 49
2.5 Dynamic Feedback Control I......Page 51
2.5.1 Parameterization......Page 53
2.5.2 Design Procedure......Page 54
2.5.3 Example 2.3......Page 56
2.6 Model with Convex-Polytopic Uncertainties......Page 57
2.7.1 Quadratic Stability......Page 59
2.7.2 Additive Gain Perturbations......Page 61
2.7.3 Multiplicative Gain Perturbations......Page 62
2.7.4 Special Cases......Page 63
2.8 H∞ Control II......Page 65
2.8.1 Additive Gain Perturbations......Page 67
2.8.3 Special Case......Page 68
2.8.4 Results for Delayless Systems......Page 69
2.8.5 Example 2.6......Page 70
2.9 Dynamic Feedback Control II......Page 71
2.9.1 Guaranteed Cost Design......Page 73
2.9.2 H∞ Design......Page 75
2.9.3 Special Cases......Page 77
2.9.4 Example 2.7......Page 79
2.10.1 Resilient Feedback Control......Page 81
2.10.2 Error Dynamics......Page 82
2.10.3 Robust Stability Results......Page 84
2.10.4 Special Cases......Page 87
2.10.6 Example 2.9......Page 91
2.11 Notes and References......Page 92
3.1 Introduction......Page 93
3.2.2 Quadratic Stability......Page 94
3.3.1 Additive Gain Perturbations......Page 96
3.3.2 Multiplicative Gain Perturbations......Page 99
3.3.4 Example 3.2......Page 100
3.4 H∞ Control Synthesis......Page 101
3.5 Design Example......Page 105
3.6 Notes and References......Page 106
4.2 Continuous-Time Model......Page 109
4.2.1 Nominal Model......Page 110
4.3 Adaptive Schemes......Page 111
4.3.1 Known Perturbation Bound......Page 112
4.3.3 Unknown Gain Perturbation Bound......Page 114
4.3.4 Example 4.2......Page 116
4.4 Polytopic Model......Page 118
4.5 Design Results......Page 119
4.5.1 Known Perturbation Bound......Page 120
4.5.2 Example 4.3......Page 121
4.5.3 Unknown Gain Perturbation Bound......Page 122
4.5.5 Model Reference State Regulation......Page 124
4.5.6 Example 4.5......Page 127
4.6 Discrete-Time Model......Page 128
4.6.1 Stability and Stabilization Results......Page 129
4.7.1 Known Perturbation Bound......Page 132
4.7.2 Unknown Perturbation Bound......Page 133
4.8.1 Example 4.6......Page 134
4.8.2 Example 4.7......Page 136
4.9 Notes and References......Page 137
5.1 Introduction......Page 138
5.2 A Class of Uncertain Systems......Page 139
5.3 The Resilient Filter......Page 140
5.3.2 LMI-Based Design Conditions......Page 141
5.3.3 Special Case......Page 143
5.3.4 A Limiting Approach to Kalman Filtering......Page 144
5.3.5 Multiplicative Gain Perturbations......Page 146
5.3.7 Example 5.2......Page 147
5.4 Continuous Polytopic Systems......Page 148
5.5 The Resilient Filtering Problem......Page 149
5.5.1 Stability Results......Page 150
5.5.2 Delay-Independent Filter Synthesis......Page 152
5.5.3 Multiplicative Gain Perturbations......Page 155
5.6.1 A Descriptor Approach......Page 158
5.6.2 Extended Newton-Leibniz Approach......Page 163
5.7.1 Example 5.3......Page 170
5.7.2 Example 5.4......Page 173
5.7.3 Example 5.5......Page 174
5.7.4 Example 5.6......Page 175
5.7.5 Example 5.7......Page 176
5.8 Notes and References......Page 178
6.1 Introduction......Page 179
6.2.1 Descriptor Transformation......Page 180
6.3.1 Nominal H2 Design......Page 181
6.3.2 Resilient H2 Design......Page 184
6.3.3 Nominal H∞ Design......Page 186
6.3.5 Simultaneous Nominal H2/H∞ Design......Page 188
6.3.6 Simultaneous Resilient H2/H∞ Design......Page 189
6.3.8 Example 6.2......Page 190
6.3.9 Example 6.3......Page 191
6.4 Continuous Polytopic Systems......Page 192
6.4.1 Polytopic H2 Design......Page 193
6.4.2 Polytopic H∞ Design......Page 194
6.4.3 Simultaneous Polytopic H2/H∞ Design......Page 195
6.5.1 System Description......Page 196
6.5.2 Descriptor Model Transformation......Page 197
6.5.3 Robust Stability......Page 202
6.5.4 Nominal Feedback Stabilization......Page 203
6.5.5 Resilient Feedback Stabilization......Page 207
6.5.8 Example 6.7......Page 209
6.5.9 Time-Varying Delay-Dependent Stability......Page 210
6.5.10 Example 6.8......Page 212
6.6 Notes and References......Page 213
7.2 Nonlinear Continuous-Time Systems......Page 214
7.3.1 Robust Delay-Independent Stability......Page 215
7.3.2 Example 7.1......Page 217
7.3.3 Robust Delay-Dependent Stability......Page 218
7.3.4 Example 7.2......Page 222
7.4.1 Nominal Feedback Design......Page 223
7.4.2 Example 7.3......Page 224
7.4.4 Resilient Feedback Design......Page 226
7.4.5 Example 7.5......Page 229
7.5 Nonlinear Discrete-Time Systems......Page 230
7.6 Robust Stability......Page 231
7.7 Robust Stabilization......Page 234
7.7.2 Example 7.9......Page 236
7.7.4 Resilient Feedback Design......Page 238
7.7.5 Example 7.11......Page 241
7.8 Notes and References......Page 242
8.1.2 Inequality 2......Page 244
8.1.4 Inequality 4 (Schur Complements)......Page 245
8.2 Lemmas......Page 247
8.3.1 Basics......Page 250
8.3.2 Some Standard Problems......Page 252
8.3.3 The S-Procedure......Page 253
8.5.1 Inverse of Block Matrices......Page 254
8.5.2 Matrix Inversion Lemma......Page 255
About the Author......Page 256
back-matter.pdf......Page 257
