Outer-Synchronization Of Fractional-Order Neural Networks Via Sampling Control

Recently,the rapid development of fractional-order neural networks has shown that fractional-order neural networks are an attractive hot research topic,and fractional-order neural networks have been used successfully in different scientific and technological fields.Based on the characteristics of fractional-order system,such as more degrees of freedom,unlimited memory,etc,fractional-order system has the potential to accomplish what integer-order ones can not do.Therefore,the study of fractional-order neural networks have important practical significance.This paper mainly studies different types of fractional-order systems,under the centralized and decentralized data-sampling control,the theoretical criterions of outer-synchronization dynamics behavior are obtained through three representative network models by using the discussion methods of structure-dependence and state-dependence.The main work of this paper includes the following contents:A class of fractional-order fuzzy neural network is analyzed.According to the characteristics of fuzzy networks,the fuzzy operation is transformed into a common linear operation by using inequality technique.Under the control of data-sampling with low cost and high reliability,the heuristic results about outer-synchronization dynamics behavior are obtained.A class of fractional-order neural network with generalized piecewise constant arguments is discussed.Based on the centralized and decentralized data-sampling control,the synchronization theory of fractional-order system,and the differential equation with generalized piecewise constant arguments,the outer-synchronization results of mixed differential equations are obtained,and the theory of fractional-order system with generalized piecewise constant arguments is extended.A class of fractional-order bidirectional associative memory(BAM)neural network is explored.Combining with the relationship between the fractional-order Caputo derivative with absolute value and itself,and Gronwall inequality,the dynamics problems of fractional-order BAM neural networks by using two different approaches on structural-dependence and state-dependence control are studied,which offer a new idea about outer-synchronization results of fractional-order BAM neural networks.In this paper,through the appropriate control,reasonable sampling points are selected to realize the outer-synchronization of the network for several different fractional-order neural networks,which provide ideas for studying the dynamic behaviors of other network models,and lays a foundation for the distribution of limited energy and the maximization of data collection.