Synchronization of fractional-order reaction–diffusion neural networks with Markov parameter jumping: Asynchronous boundary quantization control

This paper tries to study the synchronization problem of a kind of fractional-order reaction–diffusion neural networks (FRDNNs) with Markov parameter jumping. Considering the spatial and parametric characteristics of the proposed Markov FRDNNs, asynchronous boundary quantization control, is applied to achieve the driven-response synchronization of the systems. In this control scheme, one actuator is placed at the spatial boundary, and two types of quantizers is used to further reduce the control energy consumption, which is economical and easier to implement than the distributed control strategies. Besides, the parameter jumping rules of the controller and system are subject to two different Markov chains, which is more general and practical. Moreover, for fractional-order Markovian systems, the continuous frequency distributed model of fractional integrator is introduced to deal with synchronization issue of the considered systems, the corresponding synchronization criteria are obtained with the help of indirect Lyapunov functionals method. Last but not least, a numerical simulation is carried out to support the proposed control methods and theoretical results.