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Nonsmooth finite-time stabilization of neural networks with discontinuous activations. (English) Zbl 1307.93353
Summary: 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.

MSC:
93D21 Adaptive or robust stabilization
92B20 Neural networks for/in biological studies, artificial life and related topics
93B51 Design techniques (robust design, computer-aided design, etc.)
93C10 Nonlinear systems in control theory
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