Identification of Quadratic System by local gradient search

In this paper, identifying quadratic system (QS) is considered. In fact, it appears that many important nonlinear multivariable processes in engineering can be modeled by this structure. To solve this identification problem, we propose a method based on a local parameterization and a gradient search. The local parameterization is orthonormal to the tangent space of the manifold representing equivalent models, therefore the directions that do not change the output error cost function are projected out of the search direction in the update rule. Consequently, the amount of the gradient calculations is reduced to the minimal value. Furthermore, we present a numerically efficient implementation of the identification method