Adaptive Dynamic Surface Control of Epileptor Model Based on Nonlinear Luenberger State Observer

Epilepsy is a prevalent neurological disorder characterized by recurrent seizures, which are sudden bursts of electrical activity in the brain. The Epileptor model is a computational model specifically created to replicate the complex dynamics of epileptic seizures. The parameters of the Epileptor model can be adjusted to simulate activities associated with some seizure classes seen in patients. Due to the closeness of this model to nonlinear systems with nonstrict feedback form and the existence of uncertainties in the model, an adaptive dynamic surface controller is chosen for control of the system. Considering that the states in the Epileptor model are not measurable and the only measurable output is the Local Field Potentials signal, a nonlinear Luenberger state observer is developed to estimate the system states. It is the first time that the Luenberger state observer is used for the Epileptor model. In this approach, Radial Basis Neural Networks are utilized to estimate the system's nonlinear dynamics. The stability of our proposed controller along with the observer is proved, and the performance is shown using simulation. Simulation results show that by using the suggested method, the output and states of the, system track their reference, value with an acceptable error.