Finite-/fixed-time synchronization for Cohen–Grossberg neural networks with discontinuous or continuous activations via periodically switching control

Abstract

This paper is concerned with finite-/fixed-time synchronization for a class of Cohen-Grossberg neural networks with discontinuous or continuous activations and mixed time delays. Based on the finite-time stability theory, Lyapunov stability theory, the concept of Filippov solution and the differential inclusion theory, some useful finite-/fixed-time synchronization sufficient conditions for the considered Cohen-Grossberg neural networks are established by designing two kinds of novel periodically switching controllers. Instead of using uninterrupted high control strength, the periodically switching controller in each period is used with high strength control in one stage and weak strength in the other. It can overcome the effects caused by the uncertainties of Filippov solution induced by discontinuous neuron activation functions and reduce the control cost. Besides, the period switching control rate is closely related to the settling time T. Finally, two numerical examples are given to demonstrate the effectiveness and feasibility of the obtained results.

Finite/fixed-time synchronization control of fuzzy inertial cellular neural networks with mixed delays

“…Assumption 1 (see Pu and Li, 2022) g j : R → R is continuous without considering the set of countable isolation points { ϱ k j } ( j = 1 , 2 ,⋯ , N ), and there exists finite left limit g j ( ϱ k j − ) and right limit g j ( ϱ k j + ) . Furthermore, within each compact interval of R , the number of jump discontinuity points of g j is limited at most.…”

“…It is noted that neural networks with discontinuous activation function are ideal models for solving constrained optimization problems, which are more common than continuous activation function. Therefore, results in Duan et al (2019a, 2019b), Pu and Li (2022), and Xu et al (2021a, 2021b) are not applicable to the finite/fixed-time synchronization of drive-response systems (3) and (5). The method used in this paper provides a useful method for studying the FTS and F-TS of other FICNNs with mixed delays and discontinuous activation function.…”

“…Meanwhile, the inertial term is the second-order term in NNs, which is different from the first-order neural network because of its higher complexity and wider application scope. Thus, the inertial NNs have received extensive attention and made important progress in the exponential stabilization(Liu and Deng, 2020; Sheng et al, 2020), finite/fixed-time synchronization (FTS/F-TS) (Alimi et al, 2019; Jian and Duan, 2020; Kong et al, 2020; Pu and Li, 2022), convergence (Wan and Jian, 2017), passivity (Wang et al, 2020), and dissipativity (Li and Cao, 2022; Zhang et al, 2018a; Zhi et al, 2019).…”

“…However, neural networks with discontinuous activation are important and often appear in applications such as switching in electrical circuits, impacting machines, dry friction, and so on (Cai et al, 2017; Wei et al, 2018). Recently, various neural network models with discontinuous activation have attracted more and more attention and achieved some important results (Duan et al, 2019b; Kong et al, 2020; Pu and Li, 2022; Yang and Cao, 2013). However, to the best of our knowledge, there is no research on the finite/fixed-time synchronization of FICNNs with mixed delays and discontinuous activation.…”

“…This paper is one of the first attempts to study finite/fixed-time synchronization of FICNNs with mixed delays and discontinuous activation. The model of FICNNs is more general than previous network models because it considers both the inertia term and the discontinuous activation function (Alimi et al, 2019; Duan et al, 2019b; Pu and Li, 2022; Wang, 2018).…”