Average-delay impulsive control for synchronization of uncertain chaotic neural networks with variable delay impulses

Area of Science:

• Neuroscience
• Control Theory
• Nonlinear Dynamics

Background:

• Chaotic Neural Networks (CNNs) exhibit complex dynamics.
• Synchronization is crucial for CNNs but challenging due to parameter uncertainty and time delays.
• Existing control methods often have restrictive delay conditions.

Purpose of the Study:

• To investigate the synchronization of uncertain chaotic neural networks (CNNs) using a delayed impulsive control strategy.
• To develop flexible synchronization criteria that accommodate parameter uncertainty and variable impulsive delays.
• To demonstrate the facilitating role of delayed impulses in achieving synchronization.

Main Methods:

• Utilized the concepts of Average Impulsive Delay (AID) and Average Impulsive Interval (AII) to manage delays holistically.
• Derived synchronization criteria based on Linear Matrix Inequalities (LMIs) under bounded parameter uncertainty.
• Relaxed constraints on the delay in impulsive control inputs for broader applicability.

Main Results:

• Established synchronization criteria for uncertain CNNs with flexible delay conditions.
• Showed that delayed impulses can effectively promote the synchronization of CNNs.
• Validated the theoretical findings through a numerical example.

Conclusions:

• The proposed delayed impulsive control approach is effective for synchronizing uncertain CNNs.
• The use of AID and AII provides a more generalized framework for handling delays.
• The relaxed delay constraints enhance the practical applicability of the synchronization method.