Abstract
Hammerstein model has been popularly applied to identify the nonlinear systems. In this paper, a Hammerstein-type neural network (HTNN) is derived to formulate the well-known Hammerstein model. The HTNN consists of a nonlinear static gain in cascade with a linear dynamic part. First, the Lipschitz criterion for order determination is derived. Second, the backpropagation algorithm for updating the network weights is presented, and the stability analysis is also drawn. Finally, simulation results show that HTNN identification approach demonstrated identification performances.
Highlights
Identification of nonlinear dynamic systems has been one of the most interesting research areas in engineering
Similar as the well-known Wiener model, Hammerstein model is well known and the most widely used for modeling of various processes [1, 2], which comprises of a static nonlinear block preceding a dynamic linear one [3]
Different from black-box models, the block-oriented model was regarded as gray-box model which has clear physical interpretation, and its steady-state part describes the gain of the system [5]
Summary
Identification of nonlinear dynamic systems has been one of the most interesting research areas in engineering. Peng and Dubay [11] proposed a Wienertype neural network to identify nonlinear dynamic processes Most of those investigations did not give the system order determination or stability analysis. In [2, 6,7,8,9], neural networks were used to formulate the system static nonlinearities of Wiener or Hammerstein models, while in our design, a multilayer neural network is used to formulate the Hammerstein model entirely; that is, the dynamic linear block and static nonlinear block of Hammerstein model were both represented by the neural network In this way, the parameters of Hammerstein model can be obtained by training HTNN using an adequate training algorithm.
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