The nature of statistical learning theory
The nature of statistical learning theory
Support vector machines for dynamic reconstruction of a chaotic system
Advances in kernel methods
Large Scale Kernel Regression via Linear Programming
Machine Learning
On the algorithmic implementation of multiclass kernel-based vector machines
The Journal of Machine Learning Research
Kernel Methods for Pattern Analysis
Kernel Methods for Pattern Analysis
A tutorial on support vector regression
Statistics and Computing
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
A clustering technique for the identification of piecewise affine systems
Automatica (Journal of IFAC)
Identification of piecewise affine systems via mixed-integer programming
Automatica (Journal of IFAC)
Brief paper: A continuous optimization framework for hybrid system identification
Automatica (Journal of IFAC)
A Survey on Methods for Modeling and Analyzing Integrated Biological Networks
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Learning nonlinear hybrid systems: from sparse optimization to support vector regression
Proceedings of the 16th international conference on Hybrid systems: computation and control
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Hybrid system identification aims at both estimating the discrete state or mode for each data point, and the submodel governing the dynamics of the continuous state for each mode. The paper proposes a new method based on kernel regression and Support Vector Machines (SVM) to tackle this problem. The resulting algorithm is able to compute both the discrete state and the submodels in a single step, independently of the discrete state sequence that generated the data. In addition to previous works, nonlinear submodels are also considered, thus extending the class of systems on which the method can be applied from PieceWise Affine (PWA) and switched linear to PieceWise Smooth (PWS) and switched nonlinear systems with unknown nonlinearities. Piecewise systems with nonlinear boundaries between the modes are also considered with some preliminary results on this issue.