A finite-time convergent dynamic system for solving online simultaneous linear equations

ABSTRACT

A new dynamic system is proposed and investigated for solving online simultaneous linear equations. Compared with the gradient-based dynamic system and the recently proposed Zhang dynamic system, the proposed dynamic system can achieve superior convergence performance (i.e. finite-time convergence) and thus is called the finite-time convergent dynamic system. In addition, the upper bound of the convergence time is derived analytically with the error bound being zero theoretically. Simulation results further indicate that the proposed dynamic system is much more efficient than the existing dynamic systems.

KEYWORDS:

• Simultaneous linear equations
• gradient-based dynamics
• Zhang dynamics (ZD)
• upper bound
• finite-time convergence

AMS SUBJECT CLASSIFICATIONS:

• 60-08
• 65C20

Acknowledgments

The author would like to thank the editors and anonymous reviewers for their valuable suggestions and constructive comments which have really helped the author improve the presentation and quality of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China (grant number 61503152), the Natural Science Foundation of Hunan Province, China (grant number 2016JJ2101), the Research Foundation of Education Bureau of Hunan Province, China (grant number 15B192), the National Natural Science Foundation of China (grant numbers 61563017, 61561022, 61363073 and 61363033), and the Research Foundation of Jishou University, China (grant numbers 2015SYJG034, JGY201643 and JG201615).