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The Recent advances in understanding of the working principles of artificial neural networks has given a tremendous boost to identification, prediction and control tools of nonlinear systems, (Narendra & Parthasarathy, 1990; Chen & Billings, 1992; Hunt et al., 1992; Miller III et al., 1992; Pao et al., 1992; Su et al., 1992; Narendra & Mukhopadhyay, 1994; Boskovic & Narendra, 1995; Ku & Lee, 1995; Baruch et al., 1996; Jin & Gupta, 1999, Haykin, 1999; Mastorocostas & Theocharis, 2006; Kazemy et all., 2007). The main network property namely the ability to approximate complex non-linear relationships without prior knowledge of the model structure makes them a very attractive alternative to the classical modeling and control techniques. This property has been proved by the universal approximation theorem, (Haykin, 1999). Among several possible network architectures the ones most widely used are the feedforward and the recurrent neural networks. In a feedforward neural network the signals are transmitted only in one direction, starting from the input layer, subsequently through the hidden layers to the output layer, which requires applying a tap delayed global feedbacks and a tap delayed inputs to achieve a nonlinear autoregressive moving average neural dynamic plant model. A recurrent neural network has local feedback connections to some of the previous layers. Such a structure is suitable alternative to the first one when the task is to model dynamic systems, and the universal approximation theorem has been proved for the recurrent neural networks too. The preferences given to recurrent neural network identification with respect to the classical methods of process identification are clearly demonstrated in the solution of the “biasvariance dilemma”, (Haykin, 1999). Furthermore, the derivation of an analytical plant model, the parameterization of that model and the Least Square solution for the unknown parameters have the following disadvantages: (a) the analytical model did not include all factors having influence to the process behavior; (b) the analytical model is derived taking into account some simplifying suppositions which not ever match; (c) the analytical model did not described all plant nonlinearities, time lags and time delays belonging to the process in hand; (d) the analytical model did not include all process and measurement noises which are sensor and actuator dependent. In (Sage, 1968) the method of invariant imbedding has been described. This method seemed to be a universal tool for simultaneous state and O pe n A cc es s D at ab as e w w w .ite ch on lin e. co m |
