A fixed-time robust controller based on zeroing neural network for generalized projective synchronization of chaotic systems

Generalized projective synchronization (GPS) as a deeply influential chaos synchronization has always attracted lots of attention. However, plenty of traditional control methods do not predict its synchronization time or have no regard for the interference of noise in practical applications. Inspired by the fact that zeroing neural network (ZNN) can solve the time-varying problems well, this paper adopts the design method of the ZNN to construct a fixed-time robust controller (FXTRC), realizing the GPS of a class of chaotic systems. The fixed -time synchronization and robustness of chaotic systems under the FXTRC are clearly demonstrated by detailed theoretical analyses. Moreover, the upper bound of the synchronization time can be calculated by introducing the Beta function when the FXTRC is applied to control the GPS of chaotic systems. Numerical simulations prove the correctness of the theoretical analyses and the superiority of the FXTRC over the previous control methods.