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
Nonlinear black-box models in system identification: mathematical foundations
Automatica (Journal of IFAC) - Special issue on trends in system identification
The MIN PFS problem and piecewise linear model estimation
Discrete Applied Mathematics - Special issue: Third ALIO-EURO meeting on applied combinatorial optimization
Journal of Global Optimization
Brief Equivalence of hybrid dynamical models
Automatica (Journal of IFAC)
A clustering technique for the identification of piecewise affine systems
Automatica (Journal of IFAC)
Learning discontinuities with products-of-sigmoids for switching between local models
ICML '05 Proceedings of the 22nd international conference on Machine learning
HSCC'07 Proceedings of the 10th international conference on Hybrid systems: computation and control
A k-plane clustering algorithm for identification of hybrid systems
ACMOS'06 Proceedings of the 8th WSEAS international conference on Automatic control, modeling & simulation
Comparison of four procedures for the identification of hybrid systems
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Identification of deterministic switched ARX systems via identification of algebraic varieties
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Identification of piecewise affine systems based on statistical clustering technique
Automatica (Journal of IFAC)
Identification of piecewise affine systems via mixed-integer programming
Automatica (Journal of IFAC)
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This paper addresses the problem of identification of piece-wise affine (PWA) models. This problem involves the estimation from data of both the parameters of the affine submodels and the partition of the PWA map. The procedure that we propose for PWA identification exploits a greedy strategy for partitioning an infeasible system of linear inequalities into a minimum number of feasible subsystems: this provides an initial clustering of the datapoints. Then a refinement procedure is applied repeatedly to the estimated clusters in order to improve both the data classification and the parameter estimation. The partition of the PWA map is finally estimated by considering pairwise the clusters of regression vectors, and by finding a separating hyperplane for each of such pairs. We show that our procedure does not require to fix a priori the number of affine submodels, which is instead automatically estimated from the data.