This book presents a differential geometric method for designing nonlinear observers for multiple types of nonlinear systems, including single and multiple outputs, fully and partially observable systems, and regular and singular dynamical systems. It is an exposition of achievements in nonlinear observer normal forms.
The book begins by discussing linear systems, introducing the concept of observability and observer design, and then explains the difficulty of those problems for nonlinear systems. After providing foundational information on the differential geometric method, the text shows how to use the method to address observer design problems. It presents methods for a variety of systems. The authors employ worked examples to illustrate the ideas presented.
Observer Design for Nonlinear Dynamical Systems will be of interest to researchers, graduate students, and industrial professionals working with control of mechanical and dynamical systems.
Author(s): Driss Boutat, Gang Zheng
Series: Lecture Notes in Control and Information Sciences, 487
Publisher: Springer
Year: 2021
Language: English
Pages: 205
City: Singapore
Preface
Contents
1 Observability and Observer for Dynamical Systems
1.1 Introduction
1.2 Observability and Observer for Linear Dynamical Systems
1.2.1 Observability Analysis
1.2.2 Observer Design
1.3 Observability and Observer for Nonlinear Dynamical Systems
1.3.1 Observability Analysis
1.3.2 Observer Design
References
2 Background on Differential Geometry
2.1 Vector Fields: Derivation and Dynamics
2.2 Lie Bracket of Vector Fields
2.3 Differential Forms
2.4 Change of Coordinates: Diffeomorphism
2.5 Integrability, Involutivity and Frobenius Theorem
References
3 Observer Normal Form with Output Injection
3.1 Problem Statement
3.2 Observer Normal Form with Output Injection
3.3 Extension to Systems with Inputs
3.4 Observer Design
3.4.1 Luenberger-Like Observer
3.4.2 Design Procedure
References
4 Observer Normal Form with Output Injection and Output Diffeomorphism
4.1 Problem Statement
4.2 Diffeomorphism on Output
4.3 Diffeomorphism for States
4.4 Observer Design
4.4.1 High-Gain Observer
4.4.2 Design Procedure
References
5 Observer Normal Form by Means of Extended Dynamics
5.1 Problem Statement
5.2 Observer Normal Form with Scalar Extended Dynamics
5.3 High-Dimensional Extension
5.4 Observer Design
5.4.1 Adaptive Observer
5.4.2 Design Procedure
References
6 Output-Depending Observer Normal Form
6.1 Problem Statement
6.2 Analysis of the Output-Depending Normal Form
6.3 Construction of New Vector Fields
6.4 Observer Design
6.4.1 Step-by-Step Sliding Mode Observer
6.4.2 Design Procedure
References
7 Extension to Nonlinear Partially Observable Dynamical Systems
7.1 Problem Statement
7.2 Necessary and Sufficient Conditions
7.3 Diffeomorphism on the Output
7.4 Observer Design
7.4.1 Homogeneous Observer
7.4.2 Design Procedure
References
8 Extension to Nonlinear Dynamical Systems with Multiple Outputs
8.1 Problem Statement
8.2 Construction of the Frame
8.3 Necessary and Sufficient Conditions
8.4 Diffeomorphism Deduction
8.5 Special Cases
8.5.1 Equal Observability Indices
8.5.2 Unequal Observability Indices
8.6 Extension to Partial Observer Normal Form with Multiple Outputs
8.6.1 Properties of Δ and Δperp
8.6.2 Transformation
8.7 Observer Design
8.7.1 Reduced-Order Luenberger-Like Observer
8.7.2 Design Procedure
References
9 Extension to Nonlinear Singular Dynamical Systems
9.1 Problem Statement
9.2 Transformation into Regular System
9.3 Necessary and Sufficient Conditions
9.4 Observer Design
9.4.1 Nonlinear Luenberger-Like Observer
9.4.2 Design Procedure
References
Appendix Index
Index
