Observers-based event-triggered adaptive fuzzy backstepping synchronization of uncertain fractional order chaotic systems.

In this paper, for a class of uncertain fractional order chaotic systems with disturbances and partially unmeasurable states, an observer-based event-triggered adaptive fuzzy backstepping synchronization control method is proposed. Fuzzy logic systems are employed to estimate unknown functions in the backstepping procedure. To avoid the explosion of the complexity problem, a fractional order command filter is designed. Simultaneously, in order to reduce the filter error and improve the synchronization accuracy, an effective error compensation mechanism is devised. In particular, a disturbance observer is devised in the case of unmeasurable states, and a state observer is established to estimate the synchronization error of the master-slave system. The designed controller can ensure that the synchronization error converges to a small neighborhood around the origin finally and all signals are semiglobal uniformly ultimately bounded, and meanwhile, it is conducive to avoiding Zeno behavior. Finally, two numerical simulations are given to verify the effectiveness and accuracy of the proposed scheme.