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A bounded-error approach to piecewise affine system identification
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This paper proposes a three-stage procedure for parametric identification of piecewise affine autoregressive exogenous (PWARX) models and imposes that the identification error is bounded by a quantity /spl delta/.Abstract:
This paper proposes a three-stage procedure for parametric identification of piecewise affine autoregressive exogenous (PWARX) models. The first stage simultaneously classifies the data points and estimates the number of submodels and the corresponding parameters by solving the partition into a minimum number of feasible subsystems (MIN PFS) problem for a suitable set of linear complementary inequalities derived from data. Second, a refinement procedure reduces misclassifications and improves parameter estimates. The third stage determines a polyhedral partition of the regressor set via two-class or multiclass linear separation techniques. As a main feature, the algorithm imposes that the identification error is bounded by a quantity /spl delta/. Such a bound is a useful tuning parameter to trade off between quality of fit and model complexity. The performance of the proposed PWA system identification procedure is demonstrated via numerical examples and on experimental data from an electronic component placement process in a pick-and-place machine.read more
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References
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Support-Vector Networks
Corinna Cortes,Vladimir Vapnik +1 more
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Nonlinear black-box modeling in system identification: a unified overview
Jonas Sjöberg,Qinghua Zhang,Lennart Ljung,Albert Benveniste,Bernard Delyon,Pierre-Yves Glorennec,Håkan Hjalmarsson,Anatoli Juditsky +7 more
TL;DR: What are the common features in the different approaches, the choices that have to be made and what considerations are relevant for a successful system-identification application of these techniques are described, from a user's perspective.
Journal ArticleDOI
Nonlinear regulation: The piecewise linear approach
TL;DR: In this paper, a discrete-time piecewise linear system with next-state and output maps described by affine linear maps is presented. Butler et al. showed that the results on state and output feedback, observers, and inverses, standard for linear systems, are also applicable to PL systems.
Journal ArticleDOI
Brief Equivalence of hybrid dynamical models
TL;DR: Equivalences among five classes of hybrid systems are established, of paramount importance for transferring theoretical properties and tools from one class to another, with the consequence that for the study of a particular hybrid system that belongs to any of these classes, one can choose the most convenient hybrid modeling framework.