Low-Computational-Complexity Zeroing Neural Network Model for Solving Systems of Dynamic Nonlinear Equations
Zheng, Kangze; Li, Shuai; Zhang, Yunong (2023-09-25)
IEEE
25.09.2023
K. Zheng, S. Li and Y. Zhang, "Low-Computational-Complexity Zeroing Neural Network Model for Solving Systems of Dynamic Nonlinear Equations," in IEEE Transactions on Automatic Control, vol. 69, no. 7, pp. 4368-4379, July 2024, doi: 10.1109/TAC.2023.3319132
https://rightsstatements.org/vocab/InC/1.0/
© 2023 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists,or reuse of any copyrighted component of this work in other works.
https://rightsstatements.org/vocab/InC/1.0/
© 2023 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists,or reuse of any copyrighted component of this work in other works.
https://rightsstatements.org/vocab/InC/1.0/
Julkaisun pysyvä osoite on
https://urn.fi/URN:NBN:fi:oulu-202403212375
https://urn.fi/URN:NBN:fi:oulu-202403212375
Tiivistelmä
Abstract
Nonlinear equation systems are ubiquitous in a variety of fields, and how to tackle them has drawn much attention, especially dynamic ones. As a particular class of recurrent neural network, zeroing neural network (ZNN) takes time-derivative information into consideration, and thus, is a competent approach to dealing with dynamic problems. Hitherto, two kinds of ZNN models have been developed for solving systems of dynamic nonlinear equations. One of them is explicit, involving the computation of a pseudoinverse matrix, and the other is of implicit dynamics essentially. To address these two issues at once, a low-computational-complexity ZNN (LCCZNN) model is proposed. It does not need to compute any pseudoinverse matrix, and is in the form of explicit dynamics. Additionally, a novel activation function is presented to endow the LCCZNN model with finite-time convergence and certain robustness, which is proved rigorously by Lyapunov theory. Numerical experiments are conducted to validate the results of theoretical analyses, including the competence and robustness of the LCCZNN model. Finally, a pseudoinverse-free controller derived from the LCCZNN model is designed for a UR5 manipulator to online accomplish a trajectory-following task.
Nonlinear equation systems are ubiquitous in a variety of fields, and how to tackle them has drawn much attention, especially dynamic ones. As a particular class of recurrent neural network, zeroing neural network (ZNN) takes time-derivative information into consideration, and thus, is a competent approach to dealing with dynamic problems. Hitherto, two kinds of ZNN models have been developed for solving systems of dynamic nonlinear equations. One of them is explicit, involving the computation of a pseudoinverse matrix, and the other is of implicit dynamics essentially. To address these two issues at once, a low-computational-complexity ZNN (LCCZNN) model is proposed. It does not need to compute any pseudoinverse matrix, and is in the form of explicit dynamics. Additionally, a novel activation function is presented to endow the LCCZNN model with finite-time convergence and certain robustness, which is proved rigorously by Lyapunov theory. Numerical experiments are conducted to validate the results of theoretical analyses, including the competence and robustness of the LCCZNN model. Finally, a pseudoinverse-free controller derived from the LCCZNN model is designed for a UR5 manipulator to online accomplish a trajectory-following task.
Kokoelmat
- Avoin saatavuus [34617]