State and parameter estimation of uncertain brain cortex model

Nowadays, an approximate mathematical model of the brain cortex has been used for the treatment of the first epilepsy and parkinson, and several diseases. it is assumed that the mathematical model of the cortex is an exact model. however, due to the time-varying parameters, noise and other disturbances, this model is not always valid. moreover, since it is difficult and expensive to measure some states, software based solution is aimed here. consequently, in this paper, state and parameter estimation of the brain cortex model are jointly achieved using nonlinear observers of different characteristics. the state estimation of the model was merely performed in [1]. as the nonlinear observers, extended-kalman filter (ekf), sliding-mode observer (smo) and discretization based gradient observer (dbgo) approaches are designed. the estimation of unmeasurable states and parameters are performed both for the epileptic and normal state of the mathematical model since the cortex model has normally nonlinear dynamics but it exhibits chaotic behavior in epileptic state. therefore, the estimations are provided for first normal state, then epileptic state. in computational results, it is observed that the designed nonlinear observers resulted successful estimations for unmearuable states and parameters. the estimation results and estimation performances are given to compare the nonlinear observers for noisy and noiseless cases.