Optimal reduced-order synchronization of chaotic neuron models with unknown parameters

In this paper, reduced-order synchronization of uncertain chaotic neuron models with different orders is investigated. The identifier and controller modules are designed completely independently. A modified recursive least square algorithm is used to identify the unknown parameters of the slave system, and the control module is designed based on optimal control strategy. A performance index is introduced, and by minimizing a Hamiltonian function both deviation from the desired trajectory and the needed control signal are minimized. The HR neuron model and the cable model of cylindrical cell are considered as the master and slave systems, respectively. Simulation results confirm the effectiveness of the proposed method, even in the present of parameter variations.