Regularization of orthogonal neural networks using fractional derivatives

A method of regularization of orthogonal neural networks using fractional derivatives is proposed in the paper. The cost function with a penalty for non-smoothness with fractional derivatives enabling to use a priori knowledge. The formula for network weight values which minimize the proposed cost function was derived. It was demonstrated the obtained matrix in normal equations is nonnegative-definite. The results of simulation experiments where the outlined method was used for modeling static nonlinear systems were shown.