Robust stabilization control of bifurcations in Hodgkin-Huxley model with aid of unscented Kalman filter

A stabilization control method combined with the unscented Kalman filter (UKF) is proposed to control bifurcations in Hodgkin-Huxley neuronal system which are highly related to the occurrence of many dynamical diseases. In neuronal system, usually only the membrane potential can be measured with noise, thus the existing bifurcation controllers, which require exact information of all system states, are impractical. In our method, the system states used to construct the bifurcation controller are estimated by the UKF from partial noisy measurements. The stability of the controlled closed loop system is guaranteed by Lyapunov stability theory. Simulation results demonstrate the effectiveness of the proposed method. The designed controller may have potential applications in the therapy of dynamical diseases.