Finite time stabilization of delayed neural networks

Area of Science:

• Control Theory
• Computational Neuroscience
• Systems Engineering

Background:

• Delayed Neural Networks (DNNs) are crucial in modeling complex systems.
• Finite time stabilization is essential for real-time control applications.
• Ensuring stability within a finite time frame presents significant challenges for DNNs.

Purpose of the Study:

• To investigate finite time stabilization for a class of DNNs.
• To develop general conditions for feedback control laws ensuring DNN stabilization.
• To design controllers for optimizing settling time and demonstrating effectiveness.

Main Methods:

• Derivation of general conditions for feedback control.
• Design of delay-dependent and delay-independent controllers.
• Estimation of the upper bound for settling time.
• Analysis of settling time functional extrema and design of a switched controller.
• Numerical simulations for validation.

Main Results:

• General conditions for finite time stabilization of DNNs are established.
• Two distinct controllers (delay-dependent and independent) are proposed.
• An upper bound for the settling time is estimated.
• A switched controller is designed to optimize settling time.
• Simulation results confirm the effectiveness of the proposed methods.

Conclusions:

• The proposed control strategies effectively achieve finite time stabilization for DNNs.
• The developed methods provide valuable tools for controlling complex dynamic systems with delays.
• The study contributes to the advancement of stability theory for neural networks.