用改进的差分式Hopfield网络实现线性二次型最优控制

Linear quadratic optimal control with a modified difference Hopfield neural network

为解决差分式Hopfield网络能量函数的局部极小问题,本文对之改进得到一种具有迭代学习功能的线性差分式Hopfield网络.理论分析表明,该网络具有稳定性,且稳定状态使其能量函数达到唯一极小值.基于线性差分式Hopfield网络稳定性与其能量函数收敛特性的关系,本文将该网络用于求解多变量时变系统的线性二次型最优控制问题.网络的理论设计方法表明,网络的稳态输出就是欲求的最优控制向量.数字仿真取得了与理论分析一致的实验结果.

A linear difference Hopfield neural network which has the function of iterative learning is proposed to overcome the local minimum problem of its energy function. Theoretical analysis shows that the linear Hopfield neural network is stable, and the stable state makes its energy function reach its unique minimum. On the basis of the relation between the stability of the linear difference Hopfield network and its energy function＇s convergence, the linear Hopfield network is applied to solve linear quadratic optimization control problems for multivariable time-varying systems. The theoretical design method of linear Hopfield neural network shows that its stable outputs are the desired optimal control inputs. The simulation results are in accord with theoretical analysis.