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Published on: September 23, 2025
502
Flatness-based control for generalized synchronization of chaotic systems with large dissipation and dimension
Christophe Letellier1, Ludovico Minati2,3,4, Jean-Pierre Barbot5,6
1Rouen Normandie University-CORIA, Avenue de l'Université, F-76800 Saint-Etienne du Rouvray, France.
Chaos (Woodbury, N.Y.)
|September 8, 2025
Summary
This study explores generalized synchronization between drive-response systems with different dimensions and dissipation. Increasing control gain reveals various synchronization behaviors and types, classified by system properties.
Area of Science:
- Nonlinear Dynamics and Control Systems
- Chaos Theory and Complex Systems
Background:
- Flat control laws enable imposing desired dynamics onto controlled systems.
- Generalized synchronization occurs when target dynamics differ from the controlled system, requiring sufficient control gain.
Purpose of the Study:
- To explore generalized synchronization in drive-response systems with varying dimensions and dissipation levels.
- To classify emergent synchronization types based on system properties and control gain.
Main Methods:
- Structural analysis for flat control law design.
- Investigation of drive-response systems with dimensions 2-4.
- Analysis of systems with varying dissipation (dissipative and conservative).
- Classification using Lissajous curve thickness and first-return map conjugacy.
Main Results:
- Generalized synchronization is achievable with sufficiently large control gain.
- Different relationships emerge between drive and response systems based on dimension and dissipation differences.
- Several types of generalized synchronization were identified and classified.
- Lissajous curve thickness and first-return map conjugacy served as classification criteria.
Conclusions:
- The study successfully identifies and classifies various types of generalized synchronization.
- System dimension and dissipation significantly influence synchronization behavior.
- Flat control laws provide a framework for achieving complex synchronization phenomena.
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