Synchronization for stochastic coupled networks with Lévy noise via event-triggered control

Area of Science:

• Control Systems Engineering
• Stochastic Processes
• Network Science

Background:

• Stochastic networks with delays and Lévy noise present synchronization challenges.
• Event-triggered control offers a way to reduce network workload by minimizing information updates.
• Coupling structures governed by Markov chains add complexity to network dynamics.

Purpose of the Study:

• To realize almost sure synchronization in a novel array of stochastic networks.
• To implement an event-triggered control strategy for these networks.
• To analyze the impact of delays, Lévy noise, and Markovian coupling on synchronization.

Main Methods:

• Utilizing stochastic process theory, including Markov chains and Lévy processes.
• Applying the convergence theorem of non-negative semi-martingales.
• Developing an event-triggered control methodology for discrete-time information updates.

Main Results:

• Achieved almost sure synchronization in Markovian coupled networks via event-triggered control.
• Extended synchronization results to networks with directed and asymmetric coupling structures.
• Demonstrated the exclusion of Zeno behavior, confirming practical feasibility.

Conclusions:

• The proposed event-triggered control effectively achieves almost sure synchronization in complex stochastic networks.
• The framework is robust, handling delays, Lévy noise, and asymmetric topologies.
• The practical feasibility is validated by excluding Zeno behavior and through numerical simulations.