Finite-time cluster synchronization for complex dynamical networks under FDI attack: A periodic control approach

Area of Science:

• Control Theory
• Network Science
• Cybersecurity

Background:

• Complex dynamical networks (CDNs) are susceptible to cyber attacks, specifically false data injection (FDI) attacks, which manipulate controller data.
• Achieving synchronization in CDNs under attack is crucial for reliable network operation.
• Existing control strategies may not adequately balance synchronization performance with control cost in adversarial environments.

Purpose of the Study:

• To address the finite-time cluster synchronization problem in complex dynamical networks (CDNs) under false data injection (FDI) attacks.
• To propose a novel periodic secure control (PSC) strategy that enhances synchronization while minimizing control costs.
• To derive controller gains ensuring synchronization error remains within a threshold under simultaneous external disturbances and false control signals.

Main Methods:

• A new periodic secure control (PSC) strategy is developed, featuring a periodically changing set of pinning nodes.
• Sufficient conditions are derived by analyzing the periodic characteristics of the PSC strategy.
• Controller gains are obtained by solving a proposed optimization problem.

Main Results:

• A sufficient condition is established to guarantee finite-time cluster synchronization performance under FDI attacks and external disturbances.
• The proposed PSC strategy effectively manages synchronization error within a specified threshold.
• Numerical simulations validate the effectiveness of the PSC strategy in achieving cluster synchronization under cyber attacks.

Conclusions:

• The developed periodic secure control (PSC) strategy is effective for achieving finite-time cluster synchronization in complex dynamical networks (CDNs) under false data injection (FDI) attacks.
• The PSC strategy offers a balance between synchronization performance and control cost, even in the presence of cyber threats.
• The derived conditions and optimization method provide a robust framework for designing secure and efficient controllers for networked systems.