Cai Zuo-Wei, Huang Jian-Hua, Huang Li-Hong
College of Science, National University of Defense Technology, Changsha, Hunan 410073, People's Republic of China.
School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha, Hunan 410114, People's Republic of China.
Chaos. 2017 Feb;27(2):023112. doi: 10.1063/1.4976939.
The aim of this paper is to provide a novel switching control design to solve finite-time stabilization issues of a discontinuous or switching dynamical system. In order to proceed with our analysis, we first design two kinds of switching controllers: switching adaptive controller and switching state-feedback controller. Then, we apply the proposed switching control technique to stabilize the states of delayed memristor-based neural networks (DMNNs) in finite time. Based on a famous finite-time stability theorem, the theory of differential inclusion and the generalized Lyapunov functional method, some sufficient conditions are obtained to guarantee the finite-time stabilization control of DMNNs. The feedback functions of our model are allowed to be unbounded, and the upper bounds of the settling time for stabilization are also given. Finally, the validity of designed method and the theoretical results are illustrated by numerical examples.
本文的目的是提供一种新颖的切换控制设计，以解决不连续或切换动态系统的有限时间镇定问题。为了进行我们的分析，我们首先设计两种切换控制器：切换自适应控制器和切换状态反馈控制器。然后，我们应用所提出的切换控制技术在有限时间内镇定基于延迟忆阻器的神经网络（DMNN）的状态。基于一个著名的有限时间稳定性定理、微分包含理论和广义李雅普诺夫泛函方法，获得了一些充分条件来保证DMNN的有限时间镇定控制。我们模型的反馈函数可以是无界的，并且还给出了镇定的调节时间的上界。最后，通过数值例子说明了所设计方法和理论结果的有效性。
