Adaptive Stabilization of Uncertain Cortex Dynamics Under Joint Estimates and Input Constraints

Recently, an approximate mathematical model of the cortex dynamics was introduced for treatment of the epilepsy, Parkinson's, etc., where it is found applicable in real-time applications. However, designed control methods for treatments are based on the assumption of the exact mathematical model of the cortex and full state measurements are also available. In fact, the mathematical model is not exact, full state measurements may not always possible, and the measurements are always noisy. Therefore, in this brief, an adaptive unscented Kalman filter (UKF) based optimal controller is proposed to control of uncertain cortex dynamics with a single membrane potential measurement. The unmeasurable states and uncertainty function of the dynamics are estimated using adaptive UKF with noisy output measurement that are used in the production of control signal. For the security of treatments, a constrained input signal is also proposed to apply. In numerical applications, the epileptic state of the cortex dynamics is handled and accurately stabilized to a normal state with a constrained input signal. The estimation and control results are presented for future applications of uncertain and unmeasurable cortex dynamics.