Finite-time H_∞ synchronization for complex dynamical networks with time-varying delays based on adaptive control

Area of Science:

• Control Theory
• Network Science
• Nonlinear Dynamics

Background:

• Complex dynamical networks (CDNs) often exhibit time-varying delays (TVDs) and unknown internal coupling, complicating synchronization.
• External disturbances can further destabilize network dynamics, posing significant challenges for achieving robust synchronization.
• Finite-time H∞ synchronization (H∞FTS) is crucial for applications requiring fast and stable state convergence under bounded disturbances.

Purpose of the Study:

• To develop an adaptive control strategy for achieving finite-time H∞ synchronization in complex dynamical networks.
• To address the challenges posed by time-varying delays and unknown internal coupling matrices in CDNs.
• To ensure robust synchronization performance in the presence of external disturbances.

Main Methods:

• Adaptive control theory is applied to design controllers for the synchronization task.
• A specialized Lyapunov-Krasovskii function (LKF) is developed to analyze system stability.
• Passivity theory is utilized to establish criteria for finite-time H∞ synchronization.

Main Results:

• Criteria ensuring finite-time H∞ synchronization for CDNs with TVDs and disturbances are derived.
• The proposed adaptive control method effectively handles unknown internal coupling matrices.
• The effectiveness and applicability of the approach are demonstrated through numerical examples and a Chua's circuit system.

Conclusions:

• The developed adaptive control strategy successfully achieves finite-time H∞ synchronization for complex dynamical networks.
• The methodology provides a robust solution for CDNs facing time-varying delays and external disturbances.
• The results offer valuable insights and practical tools for designing stable and efficient networked systems.