Hybrid and Networked Dynamical Systems: Modeling, Analysis and Control (Lecture Notes in Control and Information Sciences, 493)

✍ Scribed by Romain Postoyan (editor), Paolo Frasca (editor), Elena Panteley (editor), Luca Zaccarian (editor)

• Publisher: Springer
• Year: 2024
• Tongue: English
• Leaves: 336
• Category: Library

✦ Synopsis

Hybrid and Networked Dynamical Systems treats a class of systems that is ubiquitous in everyday life. From energy grids to fleets of robots or vehicles to social networks to biological networks, the same scenario arises: dynamical units interact locally through a connection graph to achieve a global task. The book shows how analysis and design tools can be adapted for control applications that combine the effects of network-induced interactions and hybrid dynamics with complex results.

Following a scene-setting introduction, the remaining 12 chapters of the book are divided into three parts and provide a unique opportunity to describe the big picture that is the culmination of years of recent research activity. The contributing authors expand on their ideas at greater length than is possible in an archival research paper and use in-depth examples to illustrate their theoretical work.

The widespread importance of hybrid and networked systems means that the book is of significant interest to academic researchers working in applied mathematics, control, and electrical, mechanical and chemical engineering and to their industrial counterparts.

✦ Table of Contents

Preface
Acknowledgements
Contents
Contributors
1 Introduction
References
Part I Networked Systems: Control and Estimation
2 Contracting Infinite-Gain Margin Feedback and Synchronization of Nonlinear Systems
2.1 Introduction
2.2 Preliminaries
2.2.1 Notation
2.2.2 Highlights on Graph Theory
2.2.3 Problem Statement
2.2.4 From Linear to Nonlinear Synchronization
2.3 Robust Contractive Feedback Design
2.3.1 Riemannian Contraction Conditions for deltaδISS
2.3.2 Infinite-Gain Margin Laws
2.3.3 New Relaxed Conditions for Infinite-Gain Margin Laws
2.4 Synchronization of Nonlinear Systems
2.4.1 Undirected Graphs and Killing Vector Condition
2.4.2 Synchronization of Two Agents with Relaxed Killing Conditions
2.4.3 Synchronization with Directed Connected Graphs
2.5 Illustration
2.6 Conclusions and Perspective
References
3 Physics-Based Output-Feedback Consensus-Formation Control of Networked Autonomous Vehicles
3.1 Introduction
3.2 Model and Problem Formulation
3.2.1 Single-Robot Model
3.2.2 The Consensus-Formation Problem
3.3 Control Architecture: State-Feedback Case
3.3.1 Consensus Control of Second-Order Systems
3.3.2 State-Feedback Consensus Control of Nonholonomic Vehicles
3.4 Control Architecture: Output-Feedback Case
3.4.1 Output-Feedback Orientation Consensus
3.4.2 Output-Feedback Position Consensus
3.5 Output-Feedback Control Under Delays
3.6 An Illustrative Case-Study
3.7 Conclusions
References
4 Relating the Network Graphs of State-Space Representations to Granger Causality Conditions
4.1 Introduction
4.2 Granger Causality and Network Graph of sLTI-SSs
4.2.1 Technical Preliminaries: Linear Stochastic Realization Theory
4.2.2 Classical Granger Causality and sLTI-SS in Block Triangular Form
4.2.3 Conditional Granger Causality and sLTI-SS in Coordinated Form
4.2.4 Granger Causality Relations and Directed Acyclic Network Graphs
4.2.5 Applications of the Theoretical Results
4.3 GB-Granger Causality and Network Graph of GBSs
4.3.1 Technical Preliminaries: GBS Realization Theory
4.3.2 Extending Granger Causality
4.3.3 GB-Granger Causality and Network Graph of GBSs
4.4 Conclusions and Future Work
References
Part II Hybrid Techniques
5 Multi-consensus Problems in Hybrid Multi-agent Systems
5.1 Introduction
5.2 Review on Continuous-Time Systems over Networks
5.2.1 Directed Graph Laplacians and Almost Equitable Partitions
5.2.2 Multi-consensus of Continuous-Time Integrators
5.3 Hybrid Multi-agent Systems
5.4 The Hybrid Network Consensus Problem
5.4.1 The Multi-consensus Clusters
5.4.2 Convergence Analysis
5.5 The Hybrid Dynamics Consensus Problem
5.5.1 The Hybrid Multi-consensus Dynamics
5.5.2 The Hybrid Coupling Design
5.6 Application to Formation Control of a Heterogeneous Multi-robot System
5.7 Toward Future Perspectives: The Example of Rendezvous of Nonholonomic Robots with Heterogeneous Sensors
5.8 Conclusions
References
6 Observer Design for Hybrid Systems with Linear Maps and Known Jump Times
6.1 Introduction
6.2 Detectability and Observability Analysis
6.2.1 Hybrid Observability Gramian
6.2.2 Observability Decomposition
6.2.3 Observability from y Subscript cyc During Flows
6.2.4 Detectability Analysis
6.3 LMI-Based Observer Design from Discrete Quadratic Detectability in Observability Decomposition
6.3.1 LMI-Based Observer Design in the zz-Coordinates
6.3.2 LMI-Based Observer Design in the xx-Coordinates
6.4 KKL-Based Observer Design from Discrete Uniform Backward Distinguishability in Observability Decomposition
6.4.1 Discrete KKL Observer Design for (6.32)
6.4.2 KKL-Based Observer Design for (6.26)
6.4.3 KKL-Based Observer Design in the left parenthesis z Subscript o Baseline comma z Subscript n o Baseline right parenthesis(zo,zno)-Coordinates
6.4.4 KKL-Based Observer Design in the xx-Coordinates
6.5 Conclusion
6.6 Appendix: Technical Lemmas
6.6.1 Exponential Stability of the Error Dynamics
6.6.2 Boundedness in Finite Time
References
7 A Joint Spectral Radius for omegaω-Regular Language-Driven Switched Linear Systems
7.1 Introduction
7.2 Switched Linear Systems Driven by omegaω-Regular Languages
7.2.1 Deterministic Büchi Automaton
7.2.2 Switched Linear Systems
7.3 omegaω-Regular Joint Spectral Radius
7.4 omegaω-Regular Language-Driven Switched Systems and rhoρ-omegaω-RJSR
7.5 Computing Upper Bounds of the rhoρ-omegaω-RJSR
7.6 Numerical Example
7.7 Conclusion
References
8 Control of Uncertain Nonlinear Fully Linearizable Systems
8.1 Introduction
8.2 The Proposed Hybrid Control Scheme
8.3 Hybrid Loop Design for Robustness in the Small
8.4 Hybrid Loop Design for Robustness in the Large
8.5 Numerical Illustration
8.5.1 Implementation
8.5.2 Example
8.6 Conclusion
References
9 Improved Synthesis of Saturating Sampled-Data Control Laws for Linear Plants
9.1 Introduction
9.2 Problem Formulation
9.3 Preliminaries
9.3.1 Stability of Hybrid Systems
9.3.2 Stability Analysis with Saturation
9.4 Synthesis of Stabilizing Controller
9.5 Polynomial Timer-Dependent Lyapunov Function
9.6 Optimization Problems
9.7 Numerical Examples
9.8 Concluding Remarks
References
Part III Emerging Trends and Approaches for Analysis and Design
10 Trends and Questions in Open Multi-agent Systems
10.1 Introduction
10.2 Illustrative Examples
10.2.1 Consensus
10.2.2 Opinion Dynamics
10.2.3 Epidemics
10.3 Modeling OMAS
10.3.1 Modeling Arrivals and Departures
10.3.2 Initial State of New Agents
10.3.3 Modeling Time Evolution
10.4 Analysis of OMAS
10.4.1 Definition of Trajectories
10.4.2 Stability and Convergence
10.4.3 Scale-Independent Quantities
10.5 Towards Algorithm Design in OMAS
10.5.1 Different Types of Objectives in OMAS
10.5.2 Fundamental Performance Limitations
10.6 Further Applications
10.6.1 Consensus
10.6.2 Distributed Optimization and Learning
10.6.3 Vehicles and Robots
10.7 Future Work
10.8 Conclusions
References
11 Layers Update of Neural Network Control via Event-Triggering Mechanism
11.1 Introduction
11.2 Modeling and Problem Statement
11.2.1 Model Description
11.2.2 Preliminary Model Analysis
11.2.3 Event-Triggering Mechanism
11.3 LMI-Based Design of ETM
11.3.1 Activation Functions as Quadratic Constraints
11.3.2 Sufficient Conditions for Stability
11.3.3 Optimization Procedure
11.4 Simulations
11.5 Conclusion
References
12 Data-Driven Stabilization of Nonlinear Systems via Taylor's Expansion
12.1 Introduction
12.2 Data-Driven Nonlinear Stabilization Problem
12.3 Data-Based Feasible Sets of Dynamics
12.4 Data-Driven Controller Design
12.5 RoA Estimation
12.5.1 Continuous-Time Systems
12.5.2 Discrete-Time Systems
12.6 Example
12.6.1 Continuous-Time Systems
12.6.2 Discrete-Time Systems
12.7 Summary
12.8 Appendix
12.8.1 Petersen's Lemma
12.8.2 Proof of Lemma 12.5.3
12.8.3 Proof of Lemma 12.5.6
12.8.4 Sum of Squares Relaxation
12.8.5 Positivstellensatz
12.8.6 Proof of Lemma 12.5.8
12.8.7 Dynamics Used for Data Generation in the Example
References
13 Harmonic Modeling and Control
13.1 Introduction
13.2 Preliminaries
13.2.1 Toeplitz Block Matrices
13.2.2 Sliding Fourier Decomposition
13.3 Harmonic Modeling
13.3.1 Harmonic Control and Pole Placement
13.3.2 Solving Harmonic Sylvester Equation
13.4 Illustrative Example
13.5 Conclusion
13.6 Appendix
References
Index