Robust Stabilization of Delayed Neural Networks: Dissipativity-Learning Approach

Area of Science:

• Control Theory
• Computational Neuroscience
• Systems Engineering

Background:

• Continuous-time delayed neural networks present challenges in robust stabilization.
• Existing methods often address specific performance metrics like H∞ or passivity separately.

Purpose of the Study:

• To develop a unified dissipativity-learning approach for robust stabilization of delayed neural networks.
• To establish a new learning algorithm guaranteeing asymptotic stability and (Q,S,R)-α-dissipativity.

Main Methods:

• Utilized a dissipativity-learning framework.
• Introduced a Lyapunov-Krasovskii functional combined with Legendre polynomials.
• Developed a novel delay-dependent linear matrix inequality (LMI) condition.

Main Results:

• A new learning algorithm for robust stabilization was successfully established.
• The algorithm guarantees both asymptotic stability and (Q,S,R)-α-dissipativity.
• The approach unifies H∞ and passivity performances within a single framework.

Conclusions:

• The proposed dissipativity-learning approach and algorithm are effective for robust stabilization.
• Demonstrative examples confirm the practical utility of the developed learning algorithm.