Identification of continuous-time nonlinear systems: The nonlinear difference equation with moving average noise (NDEMA) framework

• A unified model of continuous-time and discrete-time systems was proposed.
• A systematic framework for the identification of continuous-time systems was then developed.
• The approach can detect the model structure and estimate the model parameters of noisy nonlinear systems.
• Both simulation and experimental examples were provided.

Although a vast number of techniques for the identification of nonlinear discrete-time systems have been introduced, the identification of continuous-time nonlinear systems is still extremely difficult. In this paper, the Nonlinear Difference Equation with Moving Average noise (NDEMA) model which is a general representation of nonlinear systems and contains, as special cases, both continuous-time and discrete-time models, is first proposed. Then based on this new representation, a systematic framework for the identification of nonlinear continuous-time models is developed. The new approach can not only detect the model structure and estimate the model parameters, but also work for noisy nonlinear systems. Both simulation and experimental examples are provided to illustrate how the new approach can be applied in practice.