Iterative Model Identification of Nonlinear Systems of Unknown Structure

Control usually requires models, but obtaining suitable ones in a sensible time with the required precision and limited computational burden is not a trivial task. This is particularly true if the system is nonlinear and the model structure cannot be guided by first principles. We propose an incremental approach in which the model complexity is progressively and cautiously increased. We present an iterative system identification algorithm based on a generic class of polynomial models and utilize identification experiment design to optimize the input data applied to the system. The full systematic chain from design of experiments (via model class selection and pruning to parameter identification and model validation) is shown with the issues and challenges to be addressed during this process, such as the proper choice of the model class, the persistence of the excitation, and the curse of dimensionality of polynomial models. The method is applied to three automotive problems to show its practical use: modeling the emissions from a modern diesel engine to design a virtual sensor, the hydrodynamic brake of a combustion engine testbed, and the dynamics of an engine air path. The proposed approach enables these models to be obtained quickly and systematically.