Lecture Notes in Control and Information Sciences

By: Gildas BesanÃ§on (Editor)

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Paperback | 13 August 2007

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248 Pages

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The purpose of this fantastically useful book is to lay out an overview on possible tools for state reconstruction in nonlinear systems. Here, basic observability notions and observer structures are recalled, together with ingredients for advanced designs on this basis. The problem of state reconstruction in dynamical systems, known as observer problem, is crucial for controlling or even merely monitoring processes. For linear systems, the theory has been well established for several years, so this book attempts to tackle the problem for non-linear systems.

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An Overview On Observer Tools for Nonlinear Systems	p. 1
Introduction and Problem Statement	p. 1
Context and Motivations	p. 1
Observer Problem Statement	p. 3
Nonlinear Observability	p. 5
Geometric Conditions of Observability	p. 6
Analytic Conditions for Observability	p. 9
Nonlinear Observer Design	p. 14
Basic Structures	p. 15
Advanced Designs	p. 22
Conclusion	p. 29
Appendix: Lyapunov Tools	p. 29
References	p. 31
Uniform Observability and Observer Synthesis	p. 35
Introduction	p. 35
Canonical Form and High Gain Observer : A Single Output Case	p. 37
Observability Canonical Form for Uniformly Observable Systems	p. 38
High Gain Observer Design	p. 42
An Extension to a Simple Multi-output Canonical Form	p. 44
High Gain Observer for a Multi-output Canonical Form	p. 45
The Considered Class of Systems	p. 45
A High Gain Observer	p. 48
Uniformly Observable Structure and Observer Synthesis	p. 51
Some Observability Concepts and Related Results	p. 51
Preliminary	p. 54
Constant Gain Exponential Observer	p. 55
Extension to a More General Structure	p. 61
Uniform Observability Structure	p. 65
References	p. 69
Adaptive-Gain Observers and Applications	p. 71
Introduction	p. 71
Nonlinear Filtering	p. 74
Duncan-Mortensen-Zakaï Equation	p. 74
Extended Kalman filter	p. 80
Continuous-Discrete Stochastic Systems	p. 82
Nonlinear Observers	p. 82
Canonical Form of Observability	p. 82
High-Gain Extended Kalman Filter	p. 85
High-Gain and Non High-Gain Extended Kalman Filter	p. 88
Adaptive Gain Extended Kalman Filter	p. 90
Observer for Continuous-Discrete Systems	p. 92
A "weak" Separation Principle	p. 93
Identifiability and Identification	p. 94
Definitions	p. 94
Identifiers	p. 98
Series-Connected DC Motor	p. 98
Mathematical Model	p. 99
Observability Canonical Form	p. 100
Observer Implementation	p. 101
Simulation Parameters and Observer Tuning	p. 103
Simulation Results	p. 105
Electronical Neuron Circuit	p. 106
The Modified Fitzhugh-Nagumo Model (MFHN)	p. 107
Identifiability and Observability	p. 107
Implementation	p. 109
Results	p. 109
References	p. 112
Immersion-Based Observer Design	p. 115
Introduction	p. 115
Notation and Definitions	p. 116
Nonlinear Systems	p. 116
Observability	p. 116
Immersion	p. 117
Immersion in a State-Affine Structure	p. 118
Immersion Without Output Injection	p. 118
Immersion with Output Injection	p. 120
Immersion into a Linear Structure	p. 125
Extensions of the Immersion into a State-Affine Structure	p. 127
Observer Linearization Approach	p. 127
Immersion into a Constrained Nonlinear Structure	p. 129
A Triangular Structure for Observer Design	p. 129
Immersion of Rank-Observable Systems	p. 131
Extensions	p. 134
Conclusion	p. 137
References	p. 137
Nonlinear Moving Horizon Observers: Theory and Real-Time Implementation	p. 139
Definitions and Notation	p. 139
Technical Definitions	p. 140
The Constrained Observation Problem	p. 141
About Temporal Parametrization of Uncertainties	p. 143
Optimization Based vs Analytic Observers	p. 145
Singularities Avoidance Heuristic Scheme	p. 147
Expression of the Moving Horizon Observer	p. 148
Application to a Terpolymerization Batch Process	p. 151
Differential Form of Moving Horizon Observers	p. 157
The Post Stabilization Technique	p. 164
Examples	p. 165
Nonlinear Observer for Tilting Trains	p. 166
Simulations	p. 170
Illustrating the Benefit from Using the Post-stabilization Step	p. 171
Moving Horizon Observers with Distributed Optimization	p. 172
Conclusion	p. 177
References	p. 177
Asymptotic Analysis and Observer Design in the Theory of Nonlinear Output Regulation	p. 181
Introduction	p. 181
The Steady-State Response of a Nonlinear System	p. 183
Background	p. 183
Limit Sets	p. 184
The Steady State Behavior of a Nonlinear System	p. 187
Necessary Conditions for Output Regulation	p. 192
Sufficient Conditions for Output Regulation	p. 195
The Control Structure	p. 195
The Asymptotic Internal Model Property	p. 196
Achieving the Asymptotic Internal Model Property	p. 201
Gauthier-Kupka's Internal Model (see [6])	p. 202
Bastin-Gevers's Internal Model (see [10])	p. 203
Andrieu-Praly's Internal Model (see [24])	p. 207
References	p. 209
Parameter/Fault Estimation in Nonlinear Systems and Adaptive Observers	p. 211
Introduction and Problem Statement	p. 211
Fault Diagnosis and Parameter Estimation	p. 212
Fault Diagnosis	p. 212
Parameter Estimation	p. 213
Adaptive Observers	p. 214
Adaptive State Estimation	p. 215
Joint State and Parameter Estimation	p. 218
Conclusions	p. 221
References	p. 221
Index	p. 223
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Lecture Notes in Control and Information Sciences

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