Predefined-time cluster lag synchronization of inertial neural networks: A dynamic event-triggered control

Area of Science:

• Control Systems Engineering
• Computational Neuroscience
• Nonlinear Dynamics

Background:

• Inertial neural networks (INNs) are crucial for modeling complex dynamical systems.
• Achieving cluster lag synchronization in INNs within a predefined time presents significant control challenges.
• Existing methods often lead to complex, high-dimensional linear matrix inequalities.

Purpose of the Study:

• To develop a novel control strategy for predefined-time cluster lag synchronization in INNs.
• To design a dynamic event-triggered control scheme incorporating a time-dependent exponential scaling function.
• To establish sufficient conditions for synchronization within a specified time frame while avoiding Zeno behavior.

Main Methods:

• A dynamic event-triggered control scheme is proposed.
• A time-dependent exponential scaling function is integrated into the control design.
• Sufficient conditions are derived using low-dimensional linear matrix inequalities (LMIs).
• An additional constraint is formulated to prevent Zeno behavior.

Main Results:

• The proposed control scheme guarantees predefined-time cluster lag synchronization for INNs.
• The derived conditions are formulated as low-dimensional LMIs, simplifying verification compared to traditional methods.
• The strategy effectively precludes Zeno behavior in the closed-loop system.
• Numerical simulations confirm the control strategy's effectiveness and theoretical accuracy.

Conclusions:

• The presented approach offers an efficient and verifiable method for achieving predefined-time cluster lag synchronization in INNs.
• The low-dimensional LMI formulation significantly reduces computational complexity.
• The work contributes to the advancement of control theory for complex neural network systems.