State Synchronous Control for Nerve-cell Systems via Adaptive Faster Finite-time-stabilized Sliding Mode Method

Using a novel integral-type faster finite-time-stabilized sliding mode (IFFSSM), we developed an adaptive control scheme for solving the state synchronous control problem for two space-clamped FitzHugh-Nagumo (SFHN) nerve-cell systems under the influence of disturbances.Because of the characteristics of the SFHN nerve-cell model under the principle of electrochemistry, the special stability property of IFFSSM is that two state variables of the system are stabilized in sequence on the sliding surface.Two theorems of the stability were also provided and proven.Numerical experiments were performed.The performance of the proposed control method was validated for the future practical application to neuronal circuits.