New method for identifying finite degree Volterra series

In this paper, the identification of a class of nonlinear systems which admits input–output maps described by a finite degree Volterra series is considered. In actual fact, it appears that this class can model many important nonlinear multivariable processes not only in engineering, but also in biology, socio-economics, and ecology.To solve this identification problem, we propose a method based on local gradient search in a local parameterization of the state-space realization of finite degree Volterra series with infinite horizon. Using the local parameterization not only reduces the amount of the gradient calculations to the minimal value, but also overcomes the nonuniqueness problem of the optimal solution.Moreover, we propose a sequential projection method to provide an initial estimation of the parameters of finite degree Volterra series realization. This initial estimation is used to initialize the gradient search method.