Hybrid dynamics in large-scale logistics networks

Inhaltsverzeichnis (Table of Contents)

• Abstract
• Introduction
• Preliminaries
• Hybrid Systems
• Stability of Hybrid Systems
• Interconnected Systems
• Small Gain Theorem
• Stability Analysis of Interconnected Hybrid Systems
• ISS of Interconnected Hybrid Systems
• Mixed Small Gain Condition
• Application to Special Classes of Hybrid Systems
• Model Reduction for Large-Scale Logistics Networks
• Model Reduction Based on Network Motifs
• Structural Properties of Motifs
• Applications to Network Motifs
• Conclusion and Future Work

Zielsetzung und Themenschwerpunkte (Objectives and Key Themes)

This dissertation investigates the stability properties of interconnected hybrid systems, focusing on their application to large-scale logistics networks. The work aims to develop a robust framework for analyzing the stability of such complex systems, considering their hybrid nature and large-scale interconnectedness.

• Stability Analysis of Interconnected Hybrid Systems
• Application of Small Gain Conditions to Hybrid Systems
• Model Reduction Techniques for Large-Scale Logistics Networks
• Structure-Preserving Aggregation of Network Motifs
• Stability Characterization of Logistics Networks

Zusammenfassung der Kapitel (Chapter Summaries)

The first chapters provide an introduction to hybrid systems, their stability properties, and the interconnected systems framework. The small gain theorem, a fundamental tool for stability analysis, is introduced and extended to hybrid systems.

Chapter 4 focuses on establishing input-to-state stability (ISS) for interconnected hybrid systems. The mixed small gain condition is presented, which provides a sufficient condition for ISS and is applicable to a wide range of interconnections. The application of this condition to specific subclasses of hybrid systems, including impulsive systems and comparison systems, is discussed.

Chapter 5 introduces a model reduction approach for large-scale logistics networks. This approach leverages the aggregation of typical interconnection patterns (motifs) in the network graph, enabling a significant reduction in computational complexity for stability analysis.

Schlüsselwörter (Keywords)

This dissertation focuses on the stability analysis of large-scale logistics networks, utilizing interconnected hybrid systems and applying the small gain theorem. The key themes include input-to-state stability (ISS), mixed small gain conditions, model reduction techniques, network motifs, and structure-preserving aggregation. The research aims to contribute to a robust and efficient framework for understanding and controlling the stability of complex logistics networks.