H-Systems: Observability, Diagnosability, and Predictability of Hybrid Dynamical Systems

Description

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. 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