Solving a Consistent Extension of Least Squares Problems by Use of Hopfield Neural Network

摘要

To solve a non-linear identification problem, in the paper within the theory of recurrent neural networks an approach, proposed in the fullness of time in the literature, is used, based on a modification of the Hopfield neural network and belonging a class of methods referred as neurodynamical optimization. The entity of such an approach is search for the equilibrium point of a corresponding neural network, meanwhile the point simultaneously determines the required optimization problem solution. Within the problem statement of the present paper, the term "consistent" with regard to the Least Squares Method is used as availability of non-zero solution of the problem if there exist stochastic dependence between input and output variables (as known, conventional approach does not guarantee the availability of such a solution (corresponding examples are presented)). The presentation is preceded with a deep analysis of some similar approaches known in the literature and concerned with applying consistent, in the A.N. Kolmogorov's sense, measures of dependence of random values, with emphasizing corresponding delusions.