Utilization of fixed-time integral super twisting sliding mode controller for suppression of epileptic activity via stimulus current with DBS method

Abstract

Epileptic seizures should be controlled in a fixed time. Deep brain stimulation (DBS) has many advantages in treating neurological disorders such as epilepsy. In the present study, a fixed-time integral supertwisting sliding mode controller was proposed to apply to the Pinsky-Rinzel (PR) dynamic model via the DBS method to avoid epileptic seizures. First, the current which was generated by the electrodes implanted into the brain in the DBS method, was applied to the state variable of soma membrane potential in the PR model. Then, the proposed controller was used to the combined system including the DBS current and the PR model. Based on the results, the fixed-time sliding mode controller caused the system to approach a zero tracking error in a bounded and fixed time. In addition, the super-twisting sliding mode controller prevented chattering by producing a continuous control signal. Further, the integral sliding mode controller eliminated the singularity problem caused by derivation and made the system asymptotic stable. Finally, the tracking error of the healthy state could reach zero within 2.5 milliseconds. Thus, it is suggested that the epileptic seizures be controlled exceeding this time.