TY - GEN
T1 - Dissipative quadratizations of polynomial ODE systems
AU - Cai, Yubo
AU - Pogudin, Gleb
N1 - Publisher Copyright:
© The Author(s) 2024.
PY - 2024/1/1
Y1 - 2024/1/1
N2 - Quadratization refers to a transformation of an arbitrary system of polynomial ordinary differential equations to a system with at most quadratic right-hand side. Such a transformation unveils new variables and model structures that facilitate model analysis, simulation, and control and offer a convenient parameterization for data-driven approaches. Quadratization techniques have found applications in diverse fields, including systems theory, fluid mechanics, chemical reaction modeling, and mathematical analysis. In this study, we focus on quadratizations that preserve the stability properties of the original model, specifically dissipativity at given equilibria. This preservation is desirable in many applications of quadratization including reachability analysis and synthetic biology. We establish the existence of dissipativity-preserving quadratizations, develop an algorithm for their computation, and demonstrate it in several case studies.
AB - Quadratization refers to a transformation of an arbitrary system of polynomial ordinary differential equations to a system with at most quadratic right-hand side. Such a transformation unveils new variables and model structures that facilitate model analysis, simulation, and control and offer a convenient parameterization for data-driven approaches. Quadratization techniques have found applications in diverse fields, including systems theory, fluid mechanics, chemical reaction modeling, and mathematical analysis. In this study, we focus on quadratizations that preserve the stability properties of the original model, specifically dissipativity at given equilibria. This preservation is desirable in many applications of quadratization including reachability analysis and synthetic biology. We establish the existence of dissipativity-preserving quadratizations, develop an algorithm for their computation, and demonstrate it in several case studies.
KW - differential equations
KW - quadratization
KW - stability
KW - variable transformation
U2 - 10.1007/978-3-031-57249-4_16
DO - 10.1007/978-3-031-57249-4_16
M3 - Conference contribution
AN - SCOPUS:85192267643
SN - 9783031572487
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 323
EP - 342
BT - Tools and Algorithms for the Construction and Analysis of Systems - 30th International Conference, TACAS 2024, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2024, Proceedings
A2 - Finkbeiner, Bernd
A2 - Kovács, Laura
PB - Springer Science and Business Media Deutschland GmbH
T2 - 30th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2024, which was held as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2024
Y2 - 6 April 2024 through 11 April 2024
ER -