Optimal estimation theory for dynamic systems with set membership uncertainty: an overview
Automatica (Journal of IFAC)
Nonlinear black-box modeling in system identification: a unified overview
Automatica (Journal of IFAC) - Special issue on trends in system identification
Robust Control of Nonlinear Uncertain Systems
Robust Control of Nonlinear Uncertain Systems
A Clustering Technique for the Identification of Piecewise Affine Systems
HSCC '01 Proceedings of the 4th International Workshop on Hybrid Systems: Computation and Control
Universal approximation bounds for superpositions of a sigmoidal function
IEEE Transactions on Information Theory
Neuro-fuzzy networks and their application to fault detection of dynamical systems
Engineering Applications of Artificial Intelligence
Computation of local radius of information in SM-IBC identification of nonlinear systems
Journal of Complexity
Automatica (Journal of IFAC)
Automatica (Journal of IFAC)
Set Membership approximation theory for fast implementation of Model Predictive Control laws
Automatica (Journal of IFAC)
Brief paper: The filter design from data (FD2) problem: Nonlinear Set Membership approach
Automatica (Journal of IFAC)
Towards Robustness in Neural Network Based Fault Diagnosis
International Journal of Applied Mathematics and Computer Science - Issues in Fault Diagnosis and Fault Tolerant Control
Unified Set Membership theory for identification, prediction and filtering of nonlinear systems
Automatica (Journal of IFAC)
A combined Moving Horizon and Direct Virtual Sensor approach for constrained nonlinear estimation
Automatica (Journal of IFAC)
Environmental Modelling & Software
Direct feedback control design for nonlinear systems
Automatica (Journal of IFAC)
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In the paper the problem of identifying nonlinear dynamic systems, described in nonlinear regression form, is considered, using finite and noise-corrupted measurements. Most methods in the literature are based on the estimation of a model within a finitely parametrized model class describing the functional form of involved nonlinearities. A key problem in these methods is the proper choice of the model class, typically realized by a search, from the simplest to more complex ones (linear, bilinear, polynomial, neural networks, etc.). In this paper an alternative approach, based on a Set Membership framework is presented, not requiring assumptions on the functional form of the regression function describing the relations between measured input and output, but assuming only some information on its regularity, given by bounds on its gradient. In this way, the problem of considering approximate functional forms is circumvented. Moreover, noise is assumed to be bounded, in contrast with statistical methods, which rely on assumptions such as stationarity, ergodicity, uncorrelation, type of distribution, etc., whose validity may be difficult to test reliably and is lost in presence of approximate modeling. In this paper, necessary and sufficient conditions are given for the validation of the considered assumptions. An optimal interval estimate of the regression function is obtained, providing its uncertainty range for any assigned regressor values. The set estimate allows to derive an optimal identification algorithm, giving estimates with minimal guaranteed L"p error on the assigned domain of the regressors. The properties of the optimal estimate are investigated and its worst-case L"p identification error is evaluated. The presented approach is tested and compared with other nonlinear methods on the identification of a water heater, a mechanical system with input saturation and a vehicle with controlled suspensions.