Dynamic neural networks with hybrid structures for nonlinear system identification

Dynamic neural networks (DNNs) have important properties that make them convenient to be used together with nonlinear control approaches based on state space models and differential geometry, such as feedback linearisation. However the mapping capability of DNNs are quite limited due to their fixed structure, that is, the number of layers and the number of hidden units. An example shown in this paper has demonstrated this limitation of DNNs. The development of novel DNN structures, which has good mapping capability, is a relevant challenge being addressed in this paper. Although the structure is changed minorly only, the mapping capability of the new designed DNN in this paper has been improved dramatically. Previous work [J. Deng et al., 2005. The dynamic neural network of a hybrid structure for nonlinear system identification. In: 16th IFAC World Congress, Prague.] presents a new dynamic neural network structure which is suitable for the identification of highly nonlinear systems, which needs the outputs from the real system for training and operation. This paper presents a hybrid dynamic neural network structure which presents a similar idea of serial-parallel hybrid structure, but it uses an output from another neural network for training and operation classified as a serial-parallel model. This type of DNNs does not require the output of the plant to be used as an input to the model. This neural network has the advantages of good mapping capabilities and flexibilities in training complicated systems, compared to the existed DNNs. A theoretical proof showing how this hybrid dynamic neural network can approximate finite trajectories of general nonlinear dynamic systems is given. To illustrate the capabilities of the new structure, neural networks are trained to identify a real nonlinear 3D crane system. (C) 2012 Elsevier Ltd. All rights reserved.