A robust zeroing neural network and its applications to dynamic complex matrix equation solving and robotic...

Area of Science:

• Mathematics
• Artificial Intelligence
• Control Systems

Background:

• Dynamic complex matrix equations (DCME) are common in math and industry.
• Existing recurrent neural network (RNN) models solve DCME but fail in noisy environments.
• Real-world systems are susceptible to noise, necessitating anti-noise solutions.

Purpose of the Study:

• To propose a robust zeroing neural network (RZNN) model capable of solving DCME in noisy conditions.
• To introduce a novel activation function (NAF) to enhance noise tolerance.
• To validate the model's performance through mathematical proofs and simulations.

Main Methods:

• Development of a novel activation function (NAF).
• Design and implementation of a robust zeroing neural network (RZNN) model.
• Mathematical analysis for robustness and convergence.
• Comparative numerical simulations and application to manipulator trajectory tracking.

Main Results:

• The proposed RZNN model demonstrates superior performance in solving DCME under noisy conditions.
• Mathematical proofs confirm the model's robustness and convergence.
• Numerical simulations validate the effectiveness and superiority over existing methods.
• Successful application in manipulator trajectory tracking control.

Conclusions:

• The novel RZNN model with NAF provides an effective solution for DCME in noisy environments.
• The model exhibits proven robustness and convergence, outperforming traditional methods.
• The successful application in manipulator control highlights its practical viability.