| 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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