Nonlinear Observers and Applications (Lecture Notes in Control and Information Sciences, 363)

✍ Scribed by Gildas Besançon (editor)

• Publisher: Springer
• Year: 2007
• Tongue: English
• Leaves: 234
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Title Page
Preface
Contents
List
An Overview on Observer Tools for Nonlinear Systems
Introduction and Problem Statement
Context and Motivations
Observer Problem Statement
Nonlinear Observability
Geometric Conditions of Observability
Analytic Conditions for Observability
Nonlinear Observer Design
Basic Structures
Advanced Designs
Conclusion
Appendix: Lyapunov Tools
References
Uniform Observability and Observer Synthesis
Introduction
Canonical Form and High Gain Observer : A Single Output Case
Observability Canonical Form for Uniformly Observable Systems
High Gain Observer Design
An Extension to a Simple Multi-output Canonical Form
High Gain Observer for a Multi-output Canonical Form
The Considered Class of Systems
A High Gain Observer
Uniformly Observable Structure and Observer Synthesis
Some Observability Concepts and Related Results
Preliminary
Constant Gain Exponential Observer
Extension to a More General Structure
Uniform Observability Structure
References
Adaptive-Gain Observers and Applications
Introduction
Nonlinear Filtering
Duncan-Mortensen-Zakaï Equation
Extended Kalman filter
Continuous-Discrete Stochastic Systems
Nonlinear Observers
Canonical Form of Observability
High-Gain Extended Kalman Filter
High-Gain and Non High-Gain Extended Kalman Filter
Adaptive Gain Extended Kalman Filter
Observer for Continuous--Discrete Systems
A "weak" Separation Principle
Identifiability and Identification
Definitions
Identifiers
Series-Connected DC Motor
Mathematical Model
Observability Canonical Form
Observer Implementation
Simulation Parameters and Observer Tuning
Simulation Results
Electronical Neuron Circuit
The Modified Fitzhugh-Nagumo Model (MFHN)
Identifiability and Observability
Implementation
Results
References
Immersion-Based Observer Design
Introduction
Notation and Definitions
Nonlinear Systems
Observability
Immersion
Immersion in a State-Affine Structure
Immersion Without Output Injection
Immersion with Output Injection
Immersion into a Linear Structure
Extensions of the Immersion into a State-Affine Structure
Observer Linearization Approach
Immersion into a Constrained Nonlinear Structure
A Triangular Structure for Observer Design
Immersion of Rank-Observable Systems
Extensions
Conclusion
References
Nonlinear Moving Horizon Observers: Theory and Real-Time Implementation
Definitions and Notation
Technical Definitions
The Constrained Observation Problem
About Temporal Parametrization of Uncertainties
Optimization Based vs Analytic Observers
Singularities Avoidance Heuristic Scheme
Expression of the Moving Horizon Observer
Application to a Terpolymerization Batch Process
Differential Form of Moving Horizon Observers
The Post Stabilization Technique
Examples
Nonlinear Observer for Tilting Trains
Simulations
Illustrating the Benefit from Using the Post-stabilization Step
Moving Horizon Observers with Distributed Optimization
Conclusion
References
Asymptotic Analysis and Observer Design in the Theory of Nonlinear Output Regulation
Introduction
The Steady-State Response of a Nonlinear System
Background
Limit Sets
The Steady State Behavior of a Nonlinear System
Necessary Conditions for Output Regulation
Sufficient Conditions for Output Regulation
The Control Structure
The Asymptotic Internal Model Property
Achieving the Asymptotic Internal Model Property
Gauthier-Kupka's Internal Model (see BI03bis)
Bastin-Gevers's Internal Model (see DMI04)
Andrieu-Praly's Internal Model (see SICON06)
References
Parameter/Fault Estimation in Nonlinear Systems and Adaptive Observers
Introduction and Problem Statement
Fault Diagnosis and Parameter Estimation
Fault Diagnosis
Parameter Estimation
Adaptive Observers
Adaptive State Estimation
Joint State and Parameter Estimation
Conclusions
References
Index