Identifiability and Identification of NARX models

The main goal of the project is to study identifiability and identification of Nonlinear Auto Regressive Exogenous models (NARX-models). The project consists of three problems. The identifiability problem for continuous-time nonlinear systems has got deep and extensive treatment. Compared to the continuous time case, discrete-time systems did not get as much attention. Existing results are valid for some special classes of the systems and do not give a systematic treatment to the problem. We will provide complete characterization to the relations between the different concepts and provide constructive methods to test if the system is identifiable with respect to each concept. Second problem is related to the system identification by neural networks. The main goal of this part of the project is to show that additive NARX-model is suitable for neural networks-training and control synthesis. Third problem is to develop a general framework for the identification of systems with input and output described by high frequency complex signals. Results of the project could be applied in digital telecommunications and neighbouring areas.