This book focuses on the observability of hybrid systems. It enables the reader to determine whether and how a hybrid system’s state can be reconstructed from sometimes necessarily partial information. By explaining how available measurements can be used to deduce past and future behaviours of a system, the authors extend this study of observability to embrace the properties of diagnosability and predictability.
H-systems shows how continuous and discrete dynamics and their interaction affect the observability of this general class of hybrid systems and demonstrates that hybrid characteristics are not simply generalizations of well-known aspects of traditional dynamics. The authors identify conditions for state reconstruction, prediction and diagnosis of the occurrence of possibly faulty states. The formal approach to proving those properties for hybrid systems is accompanied by simple illustrative examples. For readers who are interested in the use of state estimation for controller design, the book also provides design methods for hybrid state observers and covers their application in some industrial cases.
The book’s tutorial approach to the various forms of observability of hybrid systems helps to make H-systems of interest to academic researchers and graduate students working in control and to practitioners using control in an industrial environment.
Author(s): Elena De Santis, Maria Domenica Di Benedetto
Series: Communications and Control Engineering
Publisher: Springer
Year: 2023
Language: English
Pages: 304
City: Cham
Preface
Intended Audience and Organization of the Book
Possible Reading Paths
Acknowledgements
Contents
Main Symbols and Notation
Main Symbols
Notation
1 Introduction
References
2 H-Systems
2.1 Definition of an H-System
2.2 H-Systems and Impulsive Systems
2.3 H-Systems and PWA Systems
2.4 More on H-Systems Modeling and Properties
2.5 Illustrative Examples
2.6 Notes and Further Reading
References
3 Discrete Structure of H-Systems and Background on Finite State Machines
3.1 Analysis of the Discrete State Space
3.2 Transformations on FSMs
3.2.1 From Mealy to Moore
3.2.2 From Partially Visible to Fully Visible Output
3.3 Notes and Further Reading
References
4 Observability, Diagnosability, and Predictability of Finite State Machines
4.1 Observability of M
4.1.1 Definitions
4.1.2 Indistinguishability Notions. The Sets Sast and Bast( )
4.1.3 Characterization of Current and Critical Location Observability of M
4.2 Diagnosability of M
4.2.1 Definition
4.2.2 The Sets Fast and ast
4.2.3 Diagnosability Characterization
4.3 Predictability of M
4.3.1 Definition
4.3.2 Predictability Characterization
4.4 Notes and Further Reading
References
5 Extending Diagnosability Properties for Finite State Machines
5.1 A Parametric Definition of Diagnosability
5.1.1 The Set ast
5.1.2 Characterization of Parametric -Diagnosability
5.1.3 Characterization of Eventual and Critical -Diagnosability
5.1.4 Examples
5.2 Notes and Further Reading
References
6 Observability of H-Systems
6.1 Observability Definition
6.2 Illustrative Examples
6.3 Notes and Further Reading
References
7 Continuous Dynamics Distinguishability
7.1 Mode Distinguishability
7.2 Transition and Switching Time Detection
7.3 The Case of Discrete-Time Systems
7.4 Identifying the Evolving Dynamical System
7.4.1 Input-Generic Distinguishability Approach
7.4.2 Residual Generation Approach
7.5 Mode Distinguishability for Systems Under Attack
7.5.1 Secure Mode Distinguishability
7.5.2 Attack Detection
7.6 Identifying the Evolving Dynamical System with Unknown Input
7.7 Comparing Distinguishability Notions
7.8 Notes and Further Reading
References
8 Enriching Discrete Information in H-Systems
8.1 Preliminary Remarks and Definitions
8.2 Enriching Procedure
8.3 An Example for Systems Under Attack
8.4 Notes and Further Reading
References
9 Observability Characterization for H-Systems
9.1 Preliminary Remarks and Assumptions
9.2 Current and Critical Location Observable H-Systems
9.2.1 Checking Current Location Observability: Purely Discrete Information
9.2.2 Checking Current Location Observability: Mixed Continuous and Discrete Information
9.2.3 Leveraging Information on Elapsed Time
9.3 Checking Observability of an LH-System
9.4 Simplifying Verification of Observability Conditions
9.4.1 Checking Observability by Traps Decomposition
9.4.2 Checking Observability by Removing Observable Components
9.4.3 Checking Observability by Removing Persistent Components
9.5 Notes and Further Reading
References
10 Relaxing the Observability Notion
10.1 Almost Always Observability
10.2 Characterizing Almost Always Observability: The Cyclic Case
10.3 Characterizing Almost Always Observability: The Case of General Topology
10.4 State Estimation
10.5 Sensors Location Design
10.6 Hybrid Systems with Known Switching Times
10.7 Examples
10.8 Notes and Further Reading
References
11 Diagnosability and Predictability for H-Systems
11.1 Definitions
11.2 Diagnosability and Predictability Analysis
11.3 Symbolic Systems Approach
11.3.1 Notation
11.3.2 Pseudo-metric Systems and Approximate Simulations
11.3.3 Approximate Diagnosability and Predictability for Pseudo-metric Systems
11.3.4 Relations Between Approximate Properties and Approximate Simulation
11.3.5 Approximate Diagnosability of Nonlinear Systems
11.3.6 Approximate Predictability of Piecewise-Affine Systems
11.3.7 Checking Approximate Diagnosability and Predictability for FSMs
11.3.8 Illustrative Examples
11.4 Notes and Further Reading
References
12 Observer Design for LH-Systems
12.1 Hybrid Observer Design
12.2 Location Observability with Purely Discrete Output Information
12.2.1 Location Observer
12.2.2 Continuous Observer
12.2.3 Observer Convergence
12.3 Location Observability with Mixed Information
12.3.1 Enriched Output Generator
12.3.2 Location Observer
12.3.3 Continuous Observer
12.3.4 Observer Convergence
12.4 Notes and Further Reading
References
13 Some Applications to Automotive Control
13.1 On-Line Identification of Engaged Gear
13.1.1 Design of the Hybrid Observer
13.1.2 Experimental Results
13.2 Driveline Elastic Behavior Control
13.3 Notes and Further Reading
References
Index
