Fixed-Time Convergent Gradient Neural Network for Solving Online Sylvester Equation

Zhiguo Tan ()
Additional contact information
Zhiguo Tan: School of Information Engineering, Guangzhou Panyu Polytechnic, Guangzhou 511483, China

Mathematics, 2022, vol. 10, issue 17, 1-13

Abstract: This paper aims at finding a fixed-time solution to the Sylvester equation by using a gradient neural network (GNN). To reach this goal, a modified sign-bi-power (msbp) function is presented and applied on a linear GNN as an activation function. Accordingly, a fixed-time convergent GNN (FTC-GNN) model is developed for solving the Sylvester equation. The upper bound of the convergence time of such an FTC-GNN model can be predetermined if parameters are given regardless of the initial conditions. This point is corroborated by a detailed theoretical analysis. In addition, the convergence time is also estimated utilizing the Lyapunov stability theory. Two examples are then simulated to demonstrate the validation of the theoretical analysis, as well as the superior convergence performance of the presented FTC-GNN model as compared to the existing GNN models.

Keywords: gradient neural network; Sylvester equation; activation function; fixed-time convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/17/3090/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/17/3090/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:17:p:3090-:d:899721

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().