Unified quantified adaptive control for multiple-time stochastic synchronization of coupled memristive neural networks

Abstract

In this paper, the multiple-time (including the finite/fixed/predefined-time) stochastic synchronization issues on coupled memristive neural networks (CMNNs) are investigated with the design of a unified quantified adaptive chattering-free control scheme. Different from the construction of the general networks model, the consideration of the coupling between not only nodes but also node dimensions such that the given model becomes more general and practical. Then based on the algebraic inequality approach and with the design of a quantified adaptive control scheme, the fixed-time (FXT) stochastic synchronization criterion for CMNNs is proposed, and the networks can be finite-time (FT) synchronous when certain parameters are changed in the unified framework. To improve the existing FXT results, gamma function is used to obtain the settling time (ST) that estimates with lower conservatism. On the basis of criterion for FXT synchronization, by adding a limited FXT gain, CMNNs can not only achieve the predefined time (PDT) stochastic synchronization according to the actual situation, but also get rid of the limitation for system and controller parameters. Last but not least, the correctness of the theoretical outcomes can be verified by numerical simulation and secure communication scheme.