Nonsmooth finite-time stabilization of neural networks with discontinuous activations.
This paper is concerned with the finite-time stabilization for a class of neural networks (NNs) with discontinuous activations. The purpose of the addressed problem is to design a discontinuous controller to stabilize the states of such neural networks in finite time. Unlike the previous works, such stabilization objective will be realized for neural networks when the activations and controllers are both discontinuous. Based on the famous finite-time stability theorem of nonlinear systems and nonsmooth analysis in mathematics, sufficient conditions are established to ensure the finite-time stability of the dynamics of NNs. Then, the upper bound of the settling time for stabilization can be estimated in two forms due to two different methods of proof. Finally, two numerical examples are given to illustrate the effectiveness of the proposed design method.
Nonlinear Dynamics Group, Department of Electrical Engineering, Yeungnam University, 214-1 Dae-Dong, Kyongsan 712-749, Republic of Korea; School of Computer Science & Technology, Jiangsu Normal University, Xuzhou 221116, China.
Xiaoyang
X
Liu
Nonlinear Dynamics Group, Department of Electrical Engineering, Yeungnam University, 214-1 Dae-Dong, Kyongsan 712-749, Republic of Korea. Electronic address: jessie@ynu.ac.kr.
Ju H
JH
Park
School of Business, Jiangsu Normal University, Xuzhou 221116, China.
Nan
N
Jiang
Department of Mathematics, Southeast University, Nanjing 210096, China; Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia.
Jinde
J
Cao
D000465:Algorithms; D016571:Neural Networks, Computer; D017711:Nonlinear Dynamics; D013995:Time
Discontinuous activation; Discontinuous controller; Finite-time stabilization; Neural network