Robust complete synchronization of electrical coupling neurons under uncertain heterogeneous disturbances using adaptive internal model

An adaptive internal model control strategy is introduced into the robust complete synchronization of two gap-junction coupled FizHugh-Nagumo (FHN) neurons under uncertain heterogeneous disturbances which satisfies some general immersion condition. The synchronization problem can be converted into a robust stabilization problem of an augmented system consisting of the original given plants and an internal model. An adaptive law is employed against uncertain disturbances to make the estimate of internal model to converge to the ideal one. Following a proper state-feedback stabilizer is designed to guarantee the asymptotic stability of the resulting closed-loop system achieved for some appointed initial condition in the state space and for all possible values of the uncertain parameter vector. Finally, the simulation results demonstrate the validity of the proposed method.