Closed-loop seizure modulation via extreme learning machine based extended state observer

Neuromodulation is a promising way in clinical treatment of epilepsy, but the existing methods cannot adjust stimulations according to patients' real-time reactions. Therefore, it is necessary to acquire a systematic and a scientific regulation method based on patients' real-time reactions. The linear active disturbance rejection control can adapt to complex epileptic dynamics and improve the epilepsy regulation, even if little model information is available, and various uncertainties and external disturbances exist. However, a linear extended state observer estimates the time-varying total disturbance with a steady-state error. To improve regulation, it is crucial to estimate the total disturbance in a more accurate manner. An extreme learning machine is capable of approximating any nonlinear function. Its initial parameter generation is more convenient, adjustable parameters are fewer, and learning speed is faster. Thus, a nonlinear time-varying function can be estimated more timely and accurately. Then, an extreme learning machine based extended state observer is proposed to get a more satisfactory total disturbance estimation and more desired closed-loop regulation. The convergence of the extreme learning machine based extended state observer is verified and the stability of the closed-loop system is analyzed. Numerical results show that the proposed extended state observer is much better than a linear extended state observer in estimating the total disturbance. It guarantees a more satisfied closed-loop neuromodulation.