参数未知神经元模型的全阶与降阶最优同步

摘要

基于Lyapunov稳定性理论、最优控制原理以及分步设计方法,为神经元系统设计了非线性反馈控制器和最优控制器.其中非线性反馈控制器能使得两个神经元系统之间的轨道误差趋于零,最优控制器使得在同步过程中所花费的能量达到最低.本文以Cable模型为例,实现了两个神经元模型的全阶最优同步;以Cable模型和Hindmarsh-Rose（HR）模型为例,实现了两个神经元模型的降阶最优同步;同时,均能有效地辨识出系统参数.最后通过数值模拟进一步验证了本方案的有效性.%Based on Lyapunov stability theory,optimal control principle and step design methodology,nonlinear feedback controller and optimal controller are designed,in which the nonlinear feedback controller makes the trajectory error between two neuron systems tend to zero,and the optimal controller makes the spent energy meet minimum,which is spent in the process of synchronizing.In this paper, the uncertain cable model is taken as an example to illustrate the full-order optimal synchronization of two neurons.The uncertain cable model and the uncertain Hindmarsh-Rose（HR） model are taken to illustrate the reduced-order optimal synchronization of two neurons.In addition,the unknown parameters are identified successfully.Numerical Simulation results show the effectiveness of the strategy further.