Neural network with time delay

A third model-based approach is neural predictive control, which is a neural network version of nonlinear model predictive control [Trajanoski and Wach, 1998]. In this approach, the neural network is used for ofif-Hne identification of a system model, which is then used to design a nonhnear model predictive controller. This design may provide suitable control of nonlinear systems with time-delays and thus maybe particularly useful in biomedical appHcations. Recent computer simulation studies have demonstrated positive results for control of insuhn dehvery [Trajanoski and Wach, 1998]. 

H. Zhang, M.O. Balaban, J.C. Principe, Improving pattern recognition of electronic nose data with time-delay neural networks. Sens. Actuators B 96,385-389 (2003)... 

An important factor in the popularity of feed-forward networks is that it has been shown that a continuous valued neural network with a continuous differentiable non-linear transfer function can approximate any continuous function arbitrarily well (Cybenko, 1989). The feedforward architecture shown in Fig. 27.1 is typically used for steady-state functional approximation or one-step-ahead dynamic prediction. However, if the model is to be used to predict also more than one time step ahead, recurrent nemal networks should be used, in which delayed outputs are used as neuron inputs... 

Zhang, W., and Dietterich, T. (1996), High-Performance Job-Shop Scheduling with a Time-delay TD(() network, Advances in Neural Information Processing Systems, MIT Press, Cambridge, MA, pp. 1025-1030. 

A time-delay-neural-network in nonlinear autoregressive with exogenous input structure (narx) for single input/output (one layer) data is chosen for the calculation of an unknown input-output-relation... 

From the structure of a neural network it can be stated that the information learned is stored in the weights of the links. For different problems different stmctures can be used. The links do not have to point in the same direction, recurrent networks, in which delayed outputs are used as inputs, are also very common for process modehng since it can describe time dependency. Also all neurons in a network can be coimected with each other. For this type of network, the input, hidden and output neurons have to be strictly defined. However, the basic principle as explained above is valid for all these networks. 

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