Free model-a new direct adaptive predictor approach

The concept of the free model is developed for identification of an unknown dynamic system, which does not require the knowledge of the mathematical model and the sampling time for the system, but uses only its input and output measurements. The approximation error is derived for the free-model approximation and the conditions for satisfactory approximation performance are discussed. Under certain conditions, it is shown that the increased free-model order does not necessarily improve the approximation performance significantly. The approximated Taylor series is derived and compared with the free-model approach. Due to their differences, it is necessary to adapt the weights in the free-model representation. When the free-model idea is implemented in a neural network, the free-model based neural network becomes a direct adaptive predictor. In identifying an unknown dynamic system, the free-model based neural network is shown to have smaller sum-squared error than the conventional neural network in the initial phase of training for a class of systems.