Pinning distributed synchronization of stochastic dynamical networks: a mixed optimization approach

Area of Science:

• Control Theory
• Network Science
• Stochastic Systems

Background:

• Nonlinear dynamical networks are susceptible to multiple stochastic disturbances.
• Achieving pinning synchronization is crucial for network stability and function.
• Existing methods for pinning synchronization have limitations.

Purpose of the Study:

• To investigate pinning synchronization in nonlinear dynamical networks with stochastic disturbances.
• To develop effective pinning schemes for improved network control.
• To derive easily verifiable criteria for achieving distributed synchronization.

Main Methods:

• Lyapunov function methods and stochastic analysis techniques were employed.
• A novel mixed optimization method (convex and evolutionary algorithms) was developed for fixed pinning.
• Theoretical analysis was used for switching pinning schemes.

Main Results:

• Easily verifiable criteria for pinning distributed synchronization were derived.
• A new mixed optimization method efficiently selects pinned nodes.
• Theoretical bounds for convergence rate and mean control gain were obtained for switching schemes.

Conclusions:

• The proposed methods enhance pinning synchronization in complex networks.
• The novel optimization approach offers advantages over existing techniques.
• Simulation results validate the effectiveness of the derived criteria and methods.