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Abstract
In this paper the problem of identifying discrete time nonlinear systems in regression form from finite and noise corrupted measurements is considered. According to the specifications about identification accuracy that may be needed, a good exploration of the regressor domain of interest has to be ensured by the experimental conditions. This problem becomes very significant for growing dimension of the regressor space, leading very easily to computational complexity problems and to inaccurate identified models. These difficulties are significantly reduced if, using information about the physical structure of the system to be identified, this can be decomposed into interacting subsystems. Using this structural information, the high-dimensional identification problem may be reduced to the identification of lower dimensional subsystems and to the estimation of their interactions. Typical cases considered in the literature are Hammerstein, Wiener and Lur'e systems, but the paper shows that the approach can be extended to more complex structures composed of many subsystems and with nonlinear dynamic blocks, using as an example the identification of a half-car model for vehicle vertical dynamics, where nonlinear suspensions and tyres are considered. Assuming that the road profile is given and that front and rear vertical accelerations are measured, an experimental setup easily realizable in actual experiments on real cars, the half-car model, is decomposed as a generalized Lur'e system, consisting of a linear MIMO system, connected in a feedback form with the two nonlinear dynamic systems through non-measured signals. An iterative identification scheme is proposed, which makes use of a set membership method for the identification of the nonlinear dynamic blocks. This method does not require assumptions on the functional form of the involved nonlinearities, thus circumventing the identification accuracy problems that may be generated by considering approximate functional forms. The numerical results demonstrate the effectiveness of the proposed approach.
Acknowledgements
This research was supported in part by Ministero dell'Università e della Ricerca Scientifica e Tecnologica under the Project ‘Robustness techniques for control of uncertain systems’ and by GM-FIAT World Wide Purchasing Italia under the Project ‘Modeling of vehicle vertical accelerations’.