A novel robust fixed-time convergent zeroing neural network for solving time-varying noise-polluted nonlinear equations

ABSTRACT

Solving nonlinear equations is a crucial step in the territories of science and engineering, as many practical problems could be mathematically described by nonlinear equations. In this paper, a novel robust fast convergence zeroing neural network (RFCZNN) by utilizing a reconstructed activation function (AF) is presented and investigated for the dynamic nonlinear equations (DNE) solving problems in predictable period. Comparing with recently reported finite-time nonlinear recurrent neural network, the presented RFCZNN solves the DNE in settled theoretical time and possesses better robustness in noise-polluted environments. Unlike the finite-time convergent neural network models, the time consumption of the presented RFCZNN in convergence process can be calculated directly by mathematics without considering modelling initial states. The comparative experimental results for solving high-order (second and third order) DNE and tracking robotic motional trail are presented separately to further represent that the proposed fixed-time convergent RFCZNN model is more robust and efficient.

Keywords:

• Nonlinear equation (NE)
• zeroing neural network (ZNN)
• robust fast convergence ZNN (RFCZNN)
• activation function (AF)
• fixed-time convergence

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 60-08
• 65C20

Acknowledgement

This work is supported by the National Natural Science Foundation of China (Grant No.61875054), Natural Science Foundation of Hunan Province (Grant No.2020JJ4315, No.2020JJ5199), Scientific Research Fund of Hunan Provincial Education Department (Grant No.20B216, No.20C0786, No.18C0296).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [grant number 61875054], Natural Science Foundation of Hunan Province [grant numbers 2020JJ4315, 2020JJ5199], Scientific Research Fund of Hunan Provincial Education Department [grant numbers 20B216, .20C0786, 18C0296].