Abstract
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.
This work is supported by the NSF grant IIS-0347456 and the research startup funds from UIUC ECE Dept. and Hopkins WSE. The authors thank Prof. R. Fossum for valuable comments and Prof. A. Juloski for providing datasets for the experiments.
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Ma, Y., Vidal, R. (2005). Identification of Deterministic Switched ARX Systems via Identification of Algebraic Varieties. In: Morari, M., Thiele, L. (eds) Hybrid Systems: Computation and Control. HSCC 2005. Lecture Notes in Computer Science, vol 3414. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31954-2_29
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DOI: https://doi.org/10.1007/978-3-540-31954-2_29
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