Advanced Studies in Pure Mathematics

Algebraic tools for the analysis of state space models

Nicolette Meshkat, Zvi Rosen, and Seth Sullivant

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Abstract

We present algebraic techniques to analyze state space models in the areas of structural identifiability, observability, and indistinguishability. While the emphasis is on surveying existing algebraic tools for studying ODE systems, we also present a variety of new results. In particular: on structural identifiability, we present a method using linear algebra to find identifiable functions of the parameters of a model for unidentifiable models. On observability, we present techniques using Gröbner bases and algebraic matroids to test algebraic observability of state space models. On indistinguishability, we present a sufficient condition for distinguishability using computational algebra and demonstrate testing indistinguishability.

Article information

Source
The 50th Anniversary of Gröbner Bases, T. Hibi, ed. (Tokyo: Mathematical Society of Japan, 2018), 171-205

Dates
Received: 31 August 2016
First available in Project Euclid: 21 September 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1537499603

Digital Object Identifier
doi:10.2969/aspm/07710171

Mathematical Reviews number (MathSciNet)
MR3839711

Zentralblatt MATH identifier
07034254

Subjects
Primary: 13P10: Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) 13P25: Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.) 05E40: Combinatorial aspects of commutative algebra 52B20: Lattice polytopes (including relations with commutative algebra and algebraic geometry) [See also 06A11, 13F20, 13Hxx]

Keywords
identifiability observability indistinguishability state space models

Citation

Meshkat, Nicolette; Rosen, Zvi; Sullivant, Seth. Algebraic tools for the analysis of state space models. The 50th Anniversary of Gröbner Bases, 171--205, Mathematical Society of Japan, Tokyo, Japan, 2018. doi:10.2969/aspm/07710171. https://projecteuclid.org/euclid.aspm/1537499603


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