Identification of nonlinear dynamical systems by recurrent high-order neural networks

Recently high-order neural networks have been recognized to possess higher capability of nonlinear function representations. This paper presents a method for identification of general nonlinear dynamical systems by recurrent high-order neural networks. We introduce a new architecture of the networks in which dynamic neurons and static neurons are arbitrarily connected through high-order connections. A procedure to determine structures of the networks is studied from the view of their capability of approximating nonlinear dynamical systems. We formulate an identification scheme as training problem of the networks and derive an efficient algorithm for adjusting not only their connection weights but also their initial states. The performance of the proposed method is shown through simulation studies.