Abstract
Robots are widely used in various engineering fields, and the solution to their trajectory tracking problem has attracted increasing attention. Such a problem can be typically transformed into a time-varying nonlinear equation (TVNE). For complex and high-precision robot trajectory tracking problems, a fast and low-error tracking solution is necessary. Therefore, a varying-parameter recurrent neural network (VPRNN) model with a modified power-type time-varying parameter is proposed for solving TVNE. An improved sign-bi-power function is selected for the activation function, then the VPRNN model achieves fixed-time convergence. Numerical comparisons with the general fixed-parameter recurrent neural network model are performed, which demonstrates the superiority of our VPRNN model. Besides, the proposed VPRNN model is successfully used to solve the trajectory tracking problem of a three-link robot, which shows its feasibility in practical applications.
This work was supported in part by the National Natural Science Foundation of China under Grant 62171274 and Grant U1933125.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Argyros, I.K., Kansal, M., Kanwar, V.: On the local convergence of an eighth-order method for solving nonlinear equations. Ann. West Univ. Timisoara Math. Comput. Sci. 54(1), 3–16 (2016)
Guo, D., Zhang, Y.: Zhang neural network for online solution of time-varying linear matrix inequality aided with an equality conversion. IEEE Trans. Neural Netw. Learn. Syst. 25(2), 370–382 (2014)
Guo, D., Zhang, Y.: ZNN for solving online time-varying linear matrix-vector inequality via equality conversion. Appl. Math. Comput. 259, 327–338 (2015)
Li, S., Chen, S., Liu, B.: Accelerating a recurrent neural network to finite-time convergence for solving time-varying Sylvester equation by using a sign-bi-power activation function. Neural Process Lett. 37, 198–205 (2013)
Li, S., Li, Y.: Nonlinearly activated neural network for solving time-varying complex sylvester equation. IEEE Trans. Cybern. 44(8), 1397–1407 (2014)
Ngoc, P.H.A., Anh, T.T.: Stability of nonlinear Volterra equations and applications. Appl. Math. Comput. 341(15), 1–14 (2019)
Shen, Y., Miao, P., Huang, Y., Shen, Y.: Finite-time stability and its application for solving time-varying Sylvester equation by recurrent neural network. Neural Process Lett. 42, 763–784 (2015)
Wang, J.: Electronic realisation of recurrent neural network for solving simultaneous linear equations. Electron. Lett. 28(5), 493–495 (2002)
Xiao, L., Zhang, Y., Dai, J., Li, J., Li, W.: New noise-tolerant ZNN models with predefined-time convergence for time-variant Sylvester equation solving. IEEE Trans. Syst. Man Cybern. Syst. 51(6), 3629–3640 (2021)
Xiao, L., Zhang, Y.: Different Zhang functions resulting in different ZNN models demonstrated via time-varying linear matrix-vector inequalities solving. Neurocomputing 121, 140–149 (2013)
Zhang, M., Zheng, B.: Accelerating noise-tolerant zeroing neural network with fixed-time convergence to solve the time-varying Sylvester equation. Automatica 135, 109998 (2022)
Zhang, Y., Ge, S.S.: Design and analysis of a general recurrent neural network model for time-varying matrix inversion. IEEE Trans. Neural Networks 16(6), 1477–1490 (2005)
Zhang, Y., Yang, M., Chen, D., Li, W., Yan, X.: Proposing, QP-unification and verification of DLSM based MKE-IIWT scheme for redundant robot manipulators. In: Proceedings. 2017 IEEE 3rd Information Technology and Mechatronics Engineering Conference, pp. 242–248 (2017)
Zhang, Z., Zheng, L., Weng, J., Mao, Y., Lu, W., Xiao, L.: A new varying-parameter recurrent neural-network for online solution of time-varying Sylvester equation. IEEE Trans. Cybern. 48(11), 3135–3148 (2018)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Zhang, M., Wu, E.Q. (2022). A VPRNN Model with Fixed-Time Convergence for Time-Varying Nonlinear Equation. In: Liu, H., et al. Intelligent Robotics and Applications. ICIRA 2022. Lecture Notes in Computer Science(), vol 13457. Springer, Cham. https://doi.org/10.1007/978-3-031-13835-5_66
Download citation
DOI: https://doi.org/10.1007/978-3-031-13835-5_66
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-13834-8
Online ISBN: 978-3-031-13835-5
eBook Packages: Computer ScienceComputer Science (R0)