Sparse Approximate Solutions to Linear Systems
SIAM Journal on Computing
Recursive identification of switched ARX systems
Automatica (Journal of IFAC)
Algebraic Identification of MIMO SARX Models
HSCC '08 Proceedings of the 11th international workshop on Hybrid Systems: Computation and Control
Identifiability of discrete-time linear switched systems
Proceedings of the 13th ACM international conference on Hybrid systems: computation and control
Conditions of optimal classification for piecewise affine regression
HSCC'03 Proceedings of the 6th 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)
Highly Robust Error Correction byConvex Programming
IEEE Transactions on Information Theory
Identification of switched linear regression models using sum-of-norms regularization
Automatica (Journal of IFAC)
Learning nonlinear hybrid systems: from sparse optimization to support vector regression
Proceedings of the 16th international conference on Hybrid systems: computation and control
Realization theory of discrete-time linear switched systems
Automatica (Journal of IFAC)
An experimental validation of a novel clustering approach to PWARX identification
Engineering Applications of Artificial Intelligence
| Hi-index | 22.15 |
The work presented in this paper is concerned with the identification of switched linear systems from input-output data. The main challenge with this problem is that the data are available only as a mixture of observations generated by a finite set of different interacting linear subsystems so that one does not know a priori which subsystem has generated which data. To overcome this difficulty, we present here a sparse optimization approach inspired by very recent developments from the community of compressed sensing. We formally pose the problem of identifying each submodel as a combinatorial @?"0 optimization problem. This is indeed an NP-hard problem which can interestingly, as shown by the recent literature, be relaxed into a (convex) @?"1-norm minimization problem. We present sufficient conditions for this relaxation to be exact. The whole identification procedure allows us to extract the parameter vectors (associated with the different subsystems) one after another without any prior clustering of the data according to their respective generating-submodels. Some simulation results are included to support the potentialities of the proposed method.