Constrained Learning in Neural Networks: Application to Stable Factorization of 2-D Polynomials

Adaptive artificial neural network techniques are introduced and applied to the factorization of 2-D second order polynomials. The proposed neural network is trained using a constrained learning algorithm that achieves minimization of the usual mean square error criterion along with simultaneous satisfaction of multiple equality and inequality constraints between the polynomial coefficients. Using this method, we are able to obtain good approximate solutions for non-factorable polynomials. By incorporating stability constraints into the formalism, our method can be successfully used for the realization of stable 2-D second order IIR filters in cascade form.