Design of Luenberger Observers for a Class of Hybrid Linear Systems
HSCC '01 Proceedings of the 4th International Workshop on Hybrid Systems: Computation and Control
Design of Observers for Hybrid Systems
HSCC '02 Proceedings of the 5th International Workshop on Hybrid Systems: Computation and Control
A greedy approach to identification of piecewise affine models
HSCC'03 Proceedings of the 6th international conference on Hybrid systems: computation and control
Observability of linear hybrid systems
HSCC'03 Proceedings of the 6th international conference on Hybrid systems: computation and control
A clustering technique for the identification of piecewise affine systems
Automatica (Journal of IFAC)
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
Switched and PieceWise Nonlinear Hybrid System Identification
HSCC '08 Proceedings of the 11th international workshop on Hybrid Systems: Computation and Control
Realization Theory for Discrete-Time Semi-algebraic Hybrid Systems
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
Brief paper: A continuous optimization framework for hybrid system identification
Automatica (Journal of IFAC)
Identification of switched linear systems via sparse optimization
Automatica (Journal of IFAC)
Hybrid-fuzzy modeling and identification
Applied Soft Computing
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We present a closed-form (linear-algebraic) solution to the identification of deterministic switched ARX systems and characterize conditions that guarantee the uniqueness of the solution. We show that the simultaneous identification of the number of ARX systems, the (possibly different) model orders, the ARX model parameters, and the switching sequence is equivalent to the identification and decomposition of a projective algebraic variety whose degree and dimension depend on the number of ARX systems and the model orders, respectively. Given an upper bound for the number of systems, our algorithm identifies the variety and the maximum orders by fitting a polynomial to the data, and the number of systems, the model parameters, and the switching sequence by differentiating this polynomial. Our method is provably correct in the deterministic case, provides a good sub-optimal solution in the stochastic case, and can handle large low-dimensional data sets (up to tens of thousands points) in a batch fashion.