Belirsiz beyin korteks modelinin durum ve parametre kestirimi

Öz

Beyin korteksinin yaklaşık modeli, günümüzde başta epilepsi, Parkinson gibi hastalıklar olmak üzere birçok hastalığın tedavisinde kullanılmaktadır. Korteks matematiksel modeli kesin olduğu kabul edilmektedir. Fakat zamanla değişen parametreler, gürültü ve diğer bozucu etkilerden dolayı bu model her zaman geçerli değildir. Ayrıca bazı durumların ölçülmesi zor ve pahalı olmasından dolayı yazılım temelli yapılması hedeflenmiştir. Dolayısıyla, bu çalışmada, belirsizlik içeren beyin korteks modelinin durum ve parametre kestirimi farklı karakteristiklere sahip doğrusal-olmayan gözetleyiciler ile beraber yapılmaktadır. Sadece durum kestirimi [1] çalışmasında yapılmıştır. Doğrusal-olmayan gözetleyici genişletilmiş Kalman filtre (EKF), kayan kip gözetleyici (SMO) ve ayrıklaştırma temelli gradyan gözetleyici (DBGO) yaklaşımları tasarlanmıştır. Ölçülemeyen durum ve belirsizlik parametresi kestirimleri normal çalışma ve epileptik durumları için yapılmaktadır. Çünkü korteks model doğrusal-olmayan dinamiklere sahiptir fakat epilepsi esnasında kaotik bir davranışa sahiptir. Bu yüzden önce normal durum çalışma sonra nöbet durumu için tahminler yapılmaktadır. Sayısal benzetimlerde tasarlanan gözetleyicilerin başarılı şekilde ölçülemeyen durum ve parametre tahminlerini yaptığı gözlenmiştir. Tahmin sonuçları ve tahmin başarım performansları tasarlanan gözetleyicileri gürültülü ve gürültüsüz durumlarda karşılaştırmak için verilmiştir.

Anahtar Kelimeler

• Korteks model,Doğrusal-olmayan gözetleyici,Durum ve parametre kestirimi,EKF,SMO,DBGO

State and parameter estimation of uncertain brain cortex model

Abstract

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.

Keywords

• Cortex model,Nonlinear observer,State and parameter estimation,EKF,SMO,DBGO

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