H-infinity Control and Estimation of State-multiplicative Linear Systems

✍ Scribed by Eli Gershon, Uri Shaked, Isaac Yaesh

• Publisher: Springer
• Year: 2005
• Tongue: English
• Leaves: 261
• Series: Lecture Notes in Control and Information Sciences
• Edition: 1st Edition.
• Category: Library

✦ Synopsis

Multiplicative noise appears in systems where the process or measurement noise levels depend on the system state vector. Such systems are relevant, for example, in radar measurements where larger ranges involve higher noise level. This monograph embodies a comprehensive survey of the relevant literature with basic problems being formulated and solved by applying various techniques including game theory, linear matrix inequalities and Lyapunov parameter-dependent functions. Topics covered include: convex H2 and H-infinity norms analysis of systems with multiplicative noise; state feedback control and state estimation of systems with multiplicative noise; dynamic and static output feedback of stochastic bilinear systems; tracking controllers for stochastic bilinear systems utilizing preview information. Various examples which demonstrate the applicability of the theory to practical control engineering problems are considered; two such examples are taken from the aerospace and guidance control areas.

✦ Table of Contents

Contents......Page 20
1
Introduction......Page 25
1.2 Stochastic H ∞ Control and Estimation Problems......Page 29
1.2.2 Stochastic H ∞ : The Continuous-time Case......Page 30
1.3.1 Asymptotic Mean Square Stability......Page 32
1.4 Game-theory Approach to Stochastic H ∞ Control......Page 33
1.5.1 Stochastic Setup: The Continuous-time Case......Page 34
1.5.2 Stochastic Setup: The Discrete-time Case......Page 35
1.6 The LMI Optimization Method......Page 36
1.7 The DLMI Method......Page 37
1.8 Nomenclature......Page 39
1.9 Abbreviations......Page 40
2.1 Introduction......Page 41
2.2 Problem Formulation......Page 42
2.3 Bounded Real Lemma for Systems with State-multiplicative Noise......Page 44
2.3.1 The Stationary BRL......Page 46
2.4 State-feedback Control of Systems with State-multiplicative Noise......Page 48
2.4.1 The In.nite-horizon State-feedback Control......Page 49
2.5 H ∞ .ltering of Systems with State-multiplicative Noise......Page 51
2.5.1 The Stationary H ∞ -.ltering Problem......Page 52
2.6 Finite-horizon Stochastic Output-feedback Control......Page 54
2.7 Stationary Stochastic Output-feedback Control......Page 60
2.8 Example: Stationary Estimation and State-feedback Control......Page 62
2.9 Conclusions......Page 63
3.1 Introduction......Page 65
3.2 Problem Formulation......Page 66
3.4 The Stochastic Filter......Page 67
3.5 The Polytopic Case......Page 70
3.6 Robust Mixed Stochastic H 2 /H∞ Filtering......Page 71
3.7 Conclusions......Page 73
4.1 Introduction......Page 75
4.2 Problem Formulation......Page 76
4.3 The State-feedback Tracking......Page 77
4.3.1 The In.nite-horizon Case......Page 83
4.4.1 BRL for Systems with State-multiplicative Noise and Tracking Signal......Page 85
4.4.2 The Output-feedback Control Solution......Page 87
4.5 Example......Page 91
4.6 Conclusions......Page 92
5.1 Introduction......Page 94
5.2 Problem Formulation......Page 95
5.2.1 The Stochastic H 2 Control Problem......Page 96
5.2.2 The Stochastic H ∞ Problem......Page 99
5.3 The Robust Stochastic H 2 Static Output-feedback controller......Page 100
5.4 The Robust H ∞ Control......Page 103
5.5 Conclusions......Page 104
6.1 Introduction......Page 106
6.2 Problem Formulation......Page 107
6.3 Application to Simpli.ed Adaptive Control......Page 110
6.5 Conclusions......Page 112
7.1 Introduction......Page 113
7.2 Problem Formulation......Page 114
7.3 The Discrete-time Stochastic BRL......Page 117
7.3.1 The Discrete-time Stochastic BRL: The Stationary Case......Page 120
7.4 Stochastic H ∞ State-feedback Control......Page 121
7.4.1 The Multiple-noise Case......Page 122
7.4.2 In.nite-horizon Stochastic H 8 State-feedback control......Page 123
7.5 Stochastic State-multiplicative H ∞ Filtering......Page 126
7.6 In.nite-horizon Stochastic Filtering......Page 129
7.7 Stochastic Output-feedback......Page 131
7.8 Stationary Stochastic Output-feedback Control......Page 135
7.9.1 Example 1: The State-feedback Case......Page 137
7.9.2 Example 2: The Output-feedback Case......Page 138
7.10 Conclusions......Page 139
8.1 Introduction......Page 141
8.2 Problem Formulation......Page 142
8.3 A BRL for Systems with Stochastic Uncertainty......Page 143
8.4 Stochastic H ∞ Filtering......Page 144
8.4.1 The Polytopic Case......Page 148
8.5 Robust Mixed Stochastic H 2 /H∞ Filtering......Page 149
8.6 Conclusions......Page 151
9.1 Introduction......Page 153
9.2 Problem Formulation......Page 154
9.2.1 State-feedback Tracking......Page 155
9.3 The State-feedback Control Tracking......Page 156
9.3.1 Preview Control Tracking Patterns......Page 163
9.3.2 State-feedback: The In.nite-horizon Case......Page 165
9.4 The Output-feedback Control Tracking......Page 168
9.4.1 BRL for Stochastic State-multiplicative Systems with Tracking Signal......Page 169
9.4.2 The Output-feedback Solution......Page 170
9.5 Example: A Stochastic Finite Preview Tracking......Page 175
9.6 Conclusions......Page 178
10.2 Problem Formulation......Page 179
10.2.1 The Stochastic H 2 Control Problem......Page 181
10.2.2 The Stochastic H ∞ Problem......Page 182
10.3 The Robust Stochastic H 2 Static Output-feedback Controller......Page 183
10.4 The Robust Stochastic H ∞ Static Output-feedback
Controller......Page 185
10.5 Example......Page 186
10.6 Conclusions......Page 187
11.1 Altitude Estimation......Page 189
11.2 Altitude Control......Page 191
11.3 Guidance-motivated Tracking Filter......Page 195
11.4 Terrain Following......Page 201
11.5 Stochastic Passivity: Adaptive Motion Control......Page 206
11.6 Finite-horizon Disturbance Attenuation: Guidance......Page 210
A.2 Stochastic Processes......Page 219
A.3 Mean Square Calculus......Page 220
A.4 Wiener Process......Page 221
A.5 White Noise......Page 222
A.6 Stochastic Di.erential Equations......Page 223
A.8 Application of Ito Lemma......Page 225
A.9 Simulation of Stochastic Di.erential Equations......Page 226
A.10 The Kalman Filter for Systems with State-multiplicative Noise......Page 227
A.11 Stochastic Stability......Page 228
B.2 Solution of the BRL via Discretization......Page 231
B.3 State-feedback Control......Page 235
B.3.1 The Uncertain Case......Page 236
B.4 Output-feedback......Page 239
B.5 Conclusions......Page 242
C.1 A BRL for Discrete-time LTV Systems......Page 243
C.2.1 H ∞ State-feedback Control......Page 245
C.2.2 Robust H ∞ State-feedback Control of Uncertain Systems......Page 246
C.2.3 The Static Output-feedback Control Problem......Page 247
C.3 Example: Robust H ∞ State-feedback Control......Page 248
C.4 Conclusions......Page 250
References......Page 252