A Modified Difference Hopfield Neural Network and Its Application

A modified difference Hopfield neural network is proposed to overcome the multiple local minimum problem of normal difference Hopfield neural network. On conditions that the modified Hopfield neural network works in a parallel mode and its interconnection weight matrix is negative, it has only one stable state, and the stable state can make its energy function reach to its only minimum. On the basis of the relation between the stability of the modified difference Hopfield network and its energy function's convergence, the modified Hopfield network is applied to solve LQ dynamic optimization control problems for time-varying systems. It can be constructed by building the equivalence between the energy function of the modified Hopfield network and the performance Index of controlled system. As a result, solving LQ dynamic optimization control problem is equivalent to operating associated modified difference Hopfield network from any initial state to the stable state that represents the desired optimal control vector. The simulation results agree well with theoretical analysis.