title: Controller design for global fixed-time synchronization of delayed neural networks with discontinuous activations.
abstract: This paper addresses the controller design problem for global fixed-time synchronization of delayed neural networks (DNNs) with discontinuous activations. To solve this problem, adaptive control and state feedback control laws are designed. Then based on the two controllers and two lemmas, the error system is proved to be globally asymptotically stable and even fixed-time stable. Moreover, some sufficient and easy checked conditions are derived to guarantee the global synchronization of drive and response systems in fixed time. It is noted that the settling time functional for fixed-time synchronization is independent on initial conditions. Our fixed-time synchronization results contain the finite-time results as the special cases by choosing different values of the two controllers. Finally, theoretical results are supported by numerical simulations.
authors.affiliation: School of Automation, China University of Geosciences, Wuhan 430074, China. Electronic address: leiminw89@126.com.
authors.forename: Leimin
authors.initials: L
authors.lastname: Wang
authors.affiliation: School of Automation, Huazhong University of Science and Technology, Wuhan 430074, China. Electronic address: zgzeng@hust.edu.cn.
authors.forename: Zhigang
authors.initials: Z
authors.lastname: Zeng
authors.affiliation: College of Mathematics and Statistics, South-Central University for Nationalities, Wuhan 430074, China. Electronic address: junhaohu74@163.com.
authors.forename: Junhao
authors.initials: J
authors.lastname: Hu
authors.affiliation: School of Automation, Huazhong University of Science and Technology, Wuhan 430074, China. Electronic address: wangxiaoping@hust.edu.cn.
authors.forename: Xiaoping
authors.initials: X
authors.lastname: Wang
mesh_terms: D000465:Algorithms; D005246:Feedback; D016571:Neural Networks, Computer; D013997:Time Factors
keywords: Adaptive control; Delayed neural networks; Discontinuous activations; Global fixed-time synchronization; State feedback control