Asynchronous Boundary Control of Markov Jump Neural Networks With Diffusion Terms

Area of Science:

• Control Theory
• Neural Networks
• Stochastic Systems

Background:

• Markov jump systems exhibit state-dependent dynamics.
• Reaction-diffusion neural networks model spatio-temporal processes.
• Asynchronous control arises from mode mismatches between system and controller.

Purpose of the Study:

• To propose a novel asynchronous boundary control design for Markov jump reaction-diffusion neural networks (MJRDNNs).
• To establish criteria for ensuring stochastic finite-time boundedness of MJRDNNs under asynchronous control.
• To guarantee H∞ performance for MJRDNNs with the proposed control strategy.

Main Methods:

• Design of a novel asynchronous boundary controller for MJRDNNs.
• Construction of a Lyapunov-Krasovskii functional.
• Application of Wirtinger-type inequality to derive stability criteria.

Main Results:

• A sufficient criterion is established for stochastic finite-time boundedness of MJRDNNs.
• A sufficient condition is derived for achieving H∞ performance.
• The effectiveness of the proposed control method is demonstrated through a numerical example.

Conclusions:

• The proposed asynchronous boundary control effectively ensures stochastic finite-time boundedness for MJRDNNs.
• The developed criteria provide a robust framework for analyzing control performance.
• The findings are validated by numerical simulations, confirming the practical applicability.