Epilepsy control in a combination of the cortical and optogenetic models using fixed time integral super twisting sliding mode controller

Epilepsy is one of the most important neurological disorders in the world. In order to suppress epileptic seizures, various control algorithms have been used. Time to control and reduce attacks and robustness of the controller against variations of pathologic parameters and unwanted oscillations are important to control epileptic seizure. In order to consider these requirements and considering that one of the methods used to suppress epileptic waves is the change in mean soma (electric) potential of the excitatory neurons, this paper applies a fixed-time integral super twisting sliding mode controller to the combination of cortical and optogenetic models. First, the ion current produced in ion channels in optogenetic method is applied to the state variable of the mean electric potential of the excitatory neurons of the cortical model and the cortical and optogenetic models are combined and the controlled voltage applied to the system is applied to neurons of the epileptic zone of the brain as optic photons via the optogenetic model. Then, the mentioned controller is applied to the hybrid model so that the healthy model is tracked by the epileptic model in a fixed time. Finally, using the fixed-time integral super twisting sliding mode controller, the convergence error of the epileptic state to the healthy state has become zero. The amplitude of the control signal is reduced compared to the classic sliding mode control and technical problems and unwanted oscillations which are the shortcomings of the classic sliding mode controller are resolved.