Hyper-Exponential Stabilization of Neural Networks by Event-Triggered Impulsive Control With Actuation Delay

Area of Science:

• Control Theory
• Artificial Intelligence
• Systems Engineering

Background:

• Neural networks (NNs) require robust stabilization methods for reliable operation.
• Event-triggered control offers efficiency by reducing continuous monitoring.
• Actuation delays and Zeno behavior pose significant challenges in control systems.

Purpose of the Study:

• To develop an event-triggered impulsive control strategy for hyper-exponential stabilization of NNs.
• To address the complexities introduced by actuation delays within the control framework.
• To preclude Zeno behavior and establish criteria for rapid system convergence.

Main Methods:

• Design of an event-triggered impulsive control scheme incorporating actuation delay.
• Introduction of a periodic-detection scheme to minimize sampling overhead.
• Rigorous mathematical formulation to guarantee Zeno behavior preclusion and stability criteria.

Main Results:

• Successful implementation of event-triggered impulsive control for NNs.
• Demonstration of hyper-exponential convergence rates under the proposed control.
• Validation of theoretical findings through numerical simulations.

Conclusions:

• The proposed event-triggered impulsive control effectively achieves hyper-exponential stabilization of NNs.
• The scheme is robust to actuation delays and rigorously avoids Zeno behavior.
• Periodic detection enhances efficiency without compromising stability or convergence speed.