Department of Mathematics, Hunan First Normal University, Changsha 410205, China; School of Mathematics, Southeast University, Nanjing, 210096, China; The Jiangsu Provincial Key Laboratory of Networked Collective Intelligence, Southeast University, Nanjing 210096, China; Changsha University of Science and Technology, Changsha, 410114, China.
School of Mathematics, Southeast University, Nanjing, 210096, China; The Jiangsu Provincial Key Laboratory of Networked Collective Intelligence, Southeast University, Nanjing 210096, China.
Neural Netw. 2019 Nov;119:249-260. doi: 10.1016/j.neunet.2019.08.021. Epub 2019 Aug 26.
This paper discusses the issue of periodicity and finite-time periodic synchronization of discontinuous complex-valued neural networks (CVNNs). Based on a modified version of Kakutani's fixed point theorem, general conditions are obtained to guarantee the periodicity of discontinuous CVNNs. Next, several criteria for finite-time periodic synchronization (FTPS) are given by using a new proposed finite-time convergence theorem. Different from the traditional convergence lemma, the estimated upper bound of the derivative of the Lyapunov function (LF) is allowed to be indefinite or even positive. In order to achieve FTPS, novel discontinuous control algorithms, including state-feedback control algorithm and generalized pinning control algorithm, are designed. In the generalized pinning control algorithm, a guideline is proposed to select neurons to pin the designed controller. Finally, two simulations are given to substantiate the main results.
本文讨论了间断复值神经网络（CVNNs）的周期性和有限时间周期同步问题。基于 Kakutani 不动点定理的一个修正形式，得到了保证间断 CVNNs 周期性的一般条件。接下来，利用一个新提出的有限时间收敛定理，给出了有限时间周期同步（FTPS）的几个判据。与传统的收敛引理不同，允许 Lyapunov 函数（LF）导数的估计上界不定甚至为正。为了实现 FTPS，设计了新颖的不连续控制算法，包括状态反馈控制算法和广义钉扎控制算法。在广义钉扎控制算法中，提出了一个准则来选择神经元来钉扎设计的控制器。最后，给出了两个仿真来验证主要结果。
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