Fractional Order T–S Fuzzy Chaotic Models for Secure EEG Signal via a Wireless Communication Protocol Using a Disturbance Observer and Sliding Mode Control Technique

In this paper, the secure communication of the electroencephalogram (EEG) signal is presented via the wireless protocol. To obtain the goal of secure communication, a new stability condition for providing a new disturbance observer (DO) to estimate the attacked signals of the secure communication system is proposed. Herein, the fractional-order calculus was used to obtain the goal of the stability design. To meet the goal of the construction of the master and slave, the fractional-order chaotic system was used. First, the Takagi-Sugeno fuzzy was used to remodel the master and slave systems with support of the Grunwald–Letnikov approximation technique from continuous time to discrete time domain. Second, the DO was equipped to the slave system to reject the unwanted on both public channels and uncertain values on the master and slave sides. Third, the sliding mode control was designed based on the given stability theorem. Fourth, the stability was provided based on Lyapunov condition. Final, the simulation by using MATLAB software and experiment by using the ESP8266 chips with the wireless communication were provided to show the effectiveness of the proposed theories.