Robust Estimation for Neural Networks With Randomly Occurring Distributed Delays and Markovian Jump Coupling

Area of Science:

• Control Systems Engineering
• Computational Neuroscience
• Networked Systems Theory

Background:

• Coupled neural networks are crucial in complex systems but susceptible to parameter uncertainties.
• Randomly occurring distributed delays can degrade system performance and stability.
• Existing state estimation methods often struggle with combined uncertainties and delays.

Purpose of the Study:

• To develop robust state estimators for coupled neural networks with parameter uncertainty and random delays.
• To enhance state estimation by utilizing the local coupling structure of the networks.
• To reduce conservatism in stability analysis and performance evaluation.

Main Methods:

• Employed a polytopic model to represent parameter uncertainty.
• Utilized Bernoulli processes to model randomly occurring distributed delays.
• Developed novel state estimators exploiting local coupling information and a Kronecker product-based augmented system.
• Introduced a new Lyapunov function dependent on polytopic uncertainty and coupling information.

Main Results:

• Established sufficient conditions for the stochastic stability and performance of the augmented estimation error system.
• Derived estimator gains based on the derived stability conditions.
• Demonstrated the effectiveness of the proposed method through a numerical example.

Conclusions:

• The proposed state estimators effectively handle parameter uncertainty and random delays in coupled neural networks.
• The novel Lyapunov function approach successfully reduces estimation conservatism.
• The method provides a robust framework for state estimation in complex networked systems.