Fuzzy Model-Based Quantitative Control for Prefixed Time Synchronization of Stochastic Reaction-Diffusion Complex Networks Under Cyber-Attacks

This paper focuses on the fuzzy model-based quantitative control for prefixed-time synchronization of reaction-diffusion (RD) complex networks under stochastic noise, cyber-attacks and saturation. Different from the existing finite/ fixed time synchronization, a concept of prefixed-time synchronization is proposed to cope with cyber-attacks and stochastic noise in the target system, rather than the common finite/fixed-time synchronization. Then, two different prefixed-time synchronization criteria are presented by designing two appropriate quantization controllers and adopting the well-known probability-density inequality and the generalized sector condition techniques. Note that the proposed quantization controller can effectively overcome the constraints of communication channel and bandwidth limitation caused by cyber-attacks. Especially, the given quantization controller does not adopt the common sign function so as to avoid the controller’s quivering behavior, which effectively reduces the conservatism. Finally, two simulation results are provided to verify the rationality and superiority of the developed control design scheme in this paper.
Note to Practitioners
—It is an indisputable fact that dynamic behaviors based on complex networks sometimes depend not only on their temporal information but also on spatial locations to a large extent, such as chemical and biological processes. Therefore, the research in this study is the complex networks with RD terms rather than the common complex networks of ordinary differential form. In addition, cyber-attacks, stochastic disturbance, actuator saturation, etc. exist widely in network systems, which are completely unavoidable. Therefore, when complex networks with reaction-diffusion terms are also affected by these factors, can they achieve synchronization? In particular, is existing fixed/finite time synchronization strategy still feasible when complex networks are suffer from stochastic disturbances rather than ordinary unknown/known bounded disturbances? These questions puzzled the authors and prompted this study.