Finite-/fixed-time synchronization for Cohen–Grossberg neural networks with discontinuous or continuous activations via periodically switching control

• Published in: Cognitive neurodynamics Vol. 16; no. 1; pp. 195 - 213
• Main Authors: Pu, Hao, Li, Fengjun
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.02.2022; Springer Nature B.V
• Subjects: Artificial Intelligence; Biochemistry; Biomedical and Life Sciences; Biomedicine; Cognitive Psychology; Computer Science; Neural networks; Neurosciences; Research Article; Stability; Switching; Synchronization; Time synchronization; Timing; Finite-/fixed-time synchronization; Periodically switching control; Discontinuous activation; Filippov solution; Mixed time delays
• ISSN: 1871-4080; 1871-4099
• DOI: 10.1007/s11571-021-09694-x

This paper is concerned with finite-/fixed-time synchronization for a class of Cohen–Grossberg neural networks with discontinuous or continuous activations and mixed time delays. Based on the finite-time stability theory, Lyapunov stability theory, the concept of Filippov solution and the differential inclusion theory, some useful finite-/fixed-time synchronization sufficient conditions for the considered Cohen–Grossberg neural networks are established by designing two kinds of novel periodically switching controllers. Instead of using uninterrupted high control strength, the periodically switching controller in each period is used with high strength control in one stage and weak strength in the other. It can overcome the effects caused by the uncertainties of Filippov solution induced by discontinuous neuron activation functions and reduce the control cost. Besides, the period switching control rate is closely related to the settling time T . Finally, two numerical examples are given to demonstrate the effectiveness and feasibility of the obtained results.