Zhang Ling-Ling, Huang Li-Hong, Cai Zuo-Wei
Department of Information Technology, Hunan Women's University, Changsha, Hunan 410002, China; College of Science, National University of Defense Technology, Changsha, Hunan 410073, China.
School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha, Hunan 410114, China.
Neural Netw. 2016 Mar;75:84-96. doi: 10.1016/j.neunet.2015.11.009. Epub 2015 Dec 17.
This paper discusses the finite-time stabilization problem for time-varying delayed neural networks (DNNs) with discontinuous activation functions. By using fixed point theory and set-valued analysis, we establish the existence theorem of equilibrium point. In order to stabilize the states of this class of discontinuous DNNs in finite time, we design two different kinds of switching controllers which are described by discontinuous functions. Under the framework of Filippov solutions, several new and effective criteria are derived to realize finite-time stabilization of discontinuous DNNs based on the famous finite-time stability theory. Besides, the upper bounds of the settling time of stabilization are estimated. Numerical examples are finally provided to illustrate the correctness of the proposed design method and theoretical results.
本文讨论了具有不连续激活函数的时变延迟神经网络（DNN）的有限时间镇定问题。通过使用不动点理论和集值分析，我们建立了平衡点的存在定理。为了在有限时间内镇定这类不连续的DNN的状态，我们设计了两种由不连续函数描述的不同类型的切换控制器。在菲利波夫解的框架下，基于著名的有限时间稳定性理论，推导了几个新的有效准则以实现不连续DNN的有限时间镇定。此外，还估计了镇定调节时间的上界。最后给出数值例子来说明所提出的设计方法和理论结果的正确性。
