A Jump-Gain Integral Recurrent Neural Network for Solving Noise-Disturbed Time-Variant Nonlinear Inequality Problems

Area of Science:

• Computational mathematics and neural networks
• Applied mathematics and control theory

Background:

• Nonlinear inequalities are fundamental in science and engineering.
• Existing methods struggle with noise and time-varying parameters in nonlinear inequality problems.

Purpose of the Study:

• To propose a novel jump-gain integral recurrent (JGIR) neural network.
• To address noise-disturbed and time-variant nonlinear inequality problems.
• To demonstrate superior performance over existing neural network approaches.

Main Methods:

• Design of an integral error function.
• Development of a neural dynamic method with a jump-gain applied to the differential equation.
• Theoretical proof of global convergence and robustness.
• Implementation of the JGIR neural network.

Main Results:

• The JGIR neural network effectively solves noise-disturbed, time-variant nonlinear inequalities.
• Computer simulations show smaller computational errors and faster convergence than modified zeroing neural networks (ZNN), noise-tolerant ZNN, and varying-parameter convergent-differential neural networks.
• The JGIR method exhibits no overshoot under disturbance.
• Physical experiments on manipulator control confirm the JGIR network's effectiveness and superiority.

Conclusions:

• The proposed JGIR neural network is a highly effective and robust solution for complex nonlinear inequality problems.
• It outperforms advanced existing methods in terms of accuracy, speed, and stability.
• The JGIR network demonstrates practical applicability through successful manipulator control experiments.