title: Robust fixed-time synchronization for uncertain complex-valued neural networks with discontinuous activation functions.
abstract: This paper is concerned with the fixed-time synchronization for a class of complex-valued neural networks in the presence of discontinuous activation functions and parameter uncertainties. Fixed-time synchronization not only claims that the considered master-slave system realizes synchronization within a finite time segment, but also requires a uniform upper bound for such time intervals for all initial synchronization errors. To accomplish the target of fixed-time synchronization, a novel feedback control procedure is designed for the slave neural networks. By means of the Filippov discontinuity theories and Lyapunov stability theories, some sufficient conditions are established for the selection of control parameters to guarantee synchronization within a fixed time, while an upper bound of the settling time is acquired as well, which allows to be modulated to predefined values independently on initial conditions. Additionally, criteria of modified controller for assurance of fixed-time anti-synchronization are also derived for the same system. An example is included to illustrate the proposed methodologies.
authors.affiliation: School of Mathematics and Research Center for Complex Systems and Network Sciences, Southeast University, Nanjing 210096, China; School of Education, Xizang Minzu University, Xianyang 712082, China. Electronic address: missdxss@163.com.
authors.forename: Xiaoshuai
authors.initials: X
authors.lastname: Ding
authors.affiliation: School of Mathematics and Research Center for Complex Systems and Network Sciences, Southeast University, Nanjing 210096, China; Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia. Electronic address: jdcao@seu.edu.cn.
authors.forename: Jinde
authors.initials: J
authors.lastname: Cao
authors.affiliation: Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia. Electronic address: aalsaedi@hotmail.com.
authors.forename: Ahmed
authors.initials: A
authors.lastname: Alsaedi
authors.affiliation: Electrical & Computer Engineering Department, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia. Electronic address: fuad_alsaadi@yahoo.com.
authors.forename: Fuad E
authors.initials: FE
authors.lastname: Alsaadi
authors.affiliation: Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia; Department of Mathematics, Quaid-I-Azam University, Islamabad 44000, Pakistan. Electronic address: tahaksag@yahoo.com.
authors.forename: Tasawar
authors.initials: T
authors.lastname: Hayat
mesh_terms: D000465:Algorithms; D003344:Cortical Synchronization; D005246:Feedback; D016571:Neural Networks, Computer; D013997:Time Factors; D035501:Uncertainty
keywords: Anti-synchronization; Complex-valued neural networks; Discontinuous activation function; Filippov solution; Robust fixed-time synchronization; Uncertainties