Scale-invariant systems realize nonlinear differential operators
Lang M, Sontag E. 2016. Scale-invariant systems realize nonlinear differential operators. ACC: American Control Conference vol. 2016–July, 7526722.
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Conference Paper
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Author
Lang, MoritzISTA;
Sontag, Eduardo
Department
Abstract
In recent years, several biomolecular systems have been shown to be scale-invariant (SI), i.e. to show the same output dynamics when exposed to geometrically scaled input signals (u → pu, p > 0) after pre-adaptation to accordingly scaled constant inputs. In this article, we show that SI systems-as well as systems invariant with respect to other input transformations-can realize nonlinear differential operators: when excited by inputs obeying functional forms characteristic for a given class of invariant systems, the systems' outputs converge to constant values directly quantifying the speed of the input.
Publishing Year
Date Published
2016-07-28
Acknowledgement
The research leading to these results has received funding from the People Programme (Marie Curie Actions) of the European Union's Seventh Framework Programme (FP7/2007-2013) under REA grant agreement n° [291734]. Work supported in part by grants AFOSR FA9550-14-1-0060 and NIH 1R01GM100473.
Volume
2016-July
Article Number
7526722
Conference
ACC: American Control Conference
Conference Location
Boston, MA, USA
Conference Date
2016-07-06 – 2016-07-08
IST-REx-ID
Cite this
Lang M, Sontag E. Scale-invariant systems realize nonlinear differential operators. In: Vol 2016-July. IEEE; 2016. doi:10.1109/ACC.2016.7526722
Lang, M., & Sontag, E. (2016). Scale-invariant systems realize nonlinear differential operators (Vol. 2016–July). Presented at the ACC: American Control Conference, Boston, MA, USA: IEEE. https://doi.org/10.1109/ACC.2016.7526722
Lang, Moritz, and Eduardo Sontag. “Scale-Invariant Systems Realize Nonlinear Differential Operators,” Vol. 2016–July. IEEE, 2016. https://doi.org/10.1109/ACC.2016.7526722.
M. Lang and E. Sontag, “Scale-invariant systems realize nonlinear differential operators,” presented at the ACC: American Control Conference, Boston, MA, USA, 2016, vol. 2016–July.
Lang M, Sontag E. 2016. Scale-invariant systems realize nonlinear differential operators. ACC: American Control Conference vol. 2016–July, 7526722.
Lang, Moritz, and Eduardo Sontag. Scale-Invariant Systems Realize Nonlinear Differential Operators. Vol. 2016–July, 7526722, IEEE, 2016, doi:10.1109/ACC.2016.7526722.
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