School of Automation, China University of Geosciences, Wuhan 430074, China.
School of Automation, Huazhong University of Science and Technology, Wuhan 430074, China.
Neural Netw. 2017 Mar;87:122-131. doi: 10.1016/j.neunet.2016.12.006. Epub 2016 Dec 23.
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.
本文针对具有不连续激活函数的时滞神经网络（DNNs）的全局固定时间同步控制器设计问题进行了研究。为了解决这个问题，设计了自适应控制和状态反馈控制律。然后，基于这两个控制器和两个引理，证明了误差系统是全局渐近稳定的，甚至是固定时间稳定的。此外，还推导出了一些充分且易于检验的条件，以保证驱动和响应系统在固定时间内的全局同步。值得注意的是，固定时间同步的 settling 时间函数与初始条件无关。我们的固定时间同步结果包含有限时间结果作为特殊情况，只需选择两个控制器的不同值即可。最后，通过数值模拟验证了理论结果。
