The problem of state reconstruction in dynamical systems, known as observer problem, is undoubtedly crucial for controlling or just monitoring processes. For linear systems, the corresponding theory has been quite well established for several years now, and the purpose of the present book is to propose an overview on possible tools in that respect for nonlinear systems. Basic observability notions and observer structures are first recalled, together with ingredients for advanced designs on this basis. A special attention is then paid to the well-known high gain techniques with a summary of various corresponding recent results. A focus on the celebrated Extended Kalman filter is also given, in the perspectives of both nonlinear filtering and high gain observers, leading to so-called adaptive-gain observers. The more specific immersion approach for observer design is then emphasized, while optimization-based methods are also presented as an alternative to analytic observers. Various practical application examples are included in those discussions, and some fields of application are further considered: first the problem of nonlinear output regulation is reformulated in a perspective of observers, and then the problem of parameter or fault estimation is briefly mentioned through some adaptive observer tools.
Author(s): Gildas Besançon
Series: Lecture Notes in Control and Information Sciences
Edition: 1
Publisher: Springer Berlin Heidelberg
Year: 2010
Language: English
Pages: 233
front-matter.PDF......Page 1
Context and Motivations......Page 10
Observer Problem Statement......Page 12
Nonlinear Observability......Page 14
Geometric Conditions of Observability......Page 15
Analytic Conditions for Observability......Page 18
Nonlinear Observer Design......Page 23
Basic Structures......Page 24
Advanced Designs......Page 31
Appendix: Lyapunov Tools......Page 38
References......Page 40
Introduction......Page 43
Canonical Form and High Gain Observer : A Single Output Case......Page 45
Observability Canonical Form for Uniformly Observable Systems......Page 46
High Gain Observer Design......Page 50
An Extension to a Simple Multi-output Canonical Form......Page 52
The Considered Class of Systems......Page 53
A High Gain Observer......Page 56
Some Observability Concepts and Related Results......Page 59
Preliminary......Page 62
Constant Gain Exponential Observer......Page 63
Extension to a More General Structure......Page 69
Uniform Observability Structure......Page 73
References......Page 77
Introduction......Page 79
Observability......Page 80
Immersion......Page 81
Immersion Without Output Injection......Page 82
Immersion with Output Injection......Page 84
Immersion into a Linear Structure......Page 89
Extensions of the Immersion into a State-Affine Structure......Page 90
Observer Linearization Approach......Page 91
A Triangular Structure for Observer Design......Page 93
Immersion of Rank-Observable Systems......Page 95
Extensions......Page 98
References......Page 101
Introduction......Page 103
Duncan-Mortensen-Zakaï Equation......Page 106
Extended Kalman filter......Page 112
Canonical Form of Observability......Page 114
High-Gain Extended Kalman Filter......Page 117
High-Gain and Non High-Gain Extended Kalman Filter......Page 120
Adaptive Gain Extended Kalman Filter......Page 122
Observer for Continuous--Discrete Systems......Page 124
A "weak" Separation Principle......Page 125
Definitions......Page 126
Series-Connected DC Motor......Page 130
Mathematical Model......Page 131
Observability Canonical Form......Page 132
Observer Implementation......Page 133
Simulation Parameters and Observer Tuning......Page 135
Simulation Results......Page 137
Electronical Neuron Circuit......Page 138
Identifiability and Observability......Page 139
Results......Page 141
References......Page 144
Introduction......Page 147
Background......Page 149
Limit Sets......Page 150
The Steady State Behavior of a Nonlinear System......Page 153
Necessary Conditions for Output Regulation......Page 158
The Control Structure......Page 161
The Asymptotic Internal Model Property......Page 162
Achieving the Asymptotic Internal Model Property......Page 167
Gauthier-Kupka's Internal Model (see BI03bis)......Page 168
Bastin-Gevers's Internal Model (see DMI04)......Page 169
Andrieu-Praly's Internal Model (see SICON06)......Page 173
References......Page 175
Definitions and Notation......Page 177
Technical Definitions......Page 178
The Constrained Observation Problem......Page 179
About Temporal Parametrization of Uncertainties......Page 181
Optimization Based vs Analytic Observers......Page 183
Singularities Avoidance Heuristic Scheme......Page 185
Expression of the Moving Horizon Observer......Page 186
Application to a Terpolymerization Batch Process......Page 189
Differential Form of Moving Horizon Observers......Page 195
The Post Stabilization Technique......Page 202
Examples......Page 203
Nonlinear Observer for Tilting Trains......Page 204
Simulations......Page 208
Illustrating the Benefit from Using the Post-stabilization Step......Page 209
Moving Horizon Observers with Distributed Optimization......Page 210
References......Page 215
Introduction and Problem Statement......Page 218
Fault Diagnosis......Page 219
Parameter Estimation......Page 220
Adaptive Observers......Page 221
Adaptive State Estimation......Page 222
Joint State and Parameter Estimation......Page 225
References......Page 228
back-matter.pdf......Page 230
Index......Page 0
