Strictly intermittent quantized control for fixed/predefined-time cluster lag synchronization of stochastic...

Area of Science:

• Complex Networks
• Control Theory
• Stochastic Systems

Background:

• Synchronization is crucial in complex systems.
• Stochastic multi-weighted complex networks (SMWCNs) present unique challenges.
• Existing control methods may be complex or inefficient.

Purpose of the Study:

• To achieve fixed-time (F-T) and predefined-time (P-T) cluster lag synchronization in SMWCNs.
• To develop a novel strictly intermittent quantized control (SIQC) strategy.
• To design simpler and more economical controllers.

Main Methods:

• Mathematical induction and reduction to absurdity for proving stability.
• Development of a novel F-T stability lemma with accurate settling time (ST) estimation.
• Design of SIQC strategies for both F-T and P-T synchronization.

Main Results:

• A novel F-T stability lemma was proven, enabling accurate ST estimation.
• Simple conditions for F-T cluster lag synchronization were derived.
• P-T cluster lag synchronization was achieved with a predefinable ST.
• The proposed controllers are more economical as they deactivate the linear part during rest intervals.

Conclusions:

• The proposed SIQC strategy effectively achieves F-T and P-T cluster lag synchronization in SMWCNs.
• The developed control approach is simpler and more cost-effective than traditional methods.
• Numerical examples validate the theoretical findings and the controller's effectiveness.