Dissipative quadratizations of polynomial ODE systems
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 offers 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.
Code (1)
Methods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
Quadratization of Symmetric Pseudo-Boolean Functions
A pseudo-Boolean function is a real-valued function $f(x)=f(x_1,x_2,\ldots,x_n)$ of $n$ binary variables; that is, a mapping from $\{0,1\}^n$ to $\mathbb{R}$. For a pseudo-Boolean function $f(x)$ on $\{0,1\}^n$, we say t…
From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators
We establish approximation and learning guarantees for Fourier neural operators (FNOs) applied to time-$T$ solution operators of dissipative evolution equations. The analysis builds on the premise that FNOs can efficient…
Learning Nonlinear Input-Output Maps with Dissipative Quantum Systems
In this paper, we develop a theory of learning nonlinear input-output maps with fading memory by dissipative quantum systems, as a quantum counterpart of the theory of approximating such maps using classical dynamical sy…
Matrix-Scheduling of QSR-Dissipative Systems
This paper considers gain-scheduling of QSR-dissipative subsystems using scheduling matrices. The corresponding QSR-dissipative properties of the overall matrix-gain-scheduled system, which depends on the QSR properties …
SchedulingThe Underlying Dynamics of Life and Its Evolution: A Prigogine-Inspired Informational Dissipative System
Life is fundamentally a scientific enigma. The interplay between chaos, entropy dynamics, and Prigogine's dissipative systems offers profound insights into the emergence, stabilization, and eventual collapse of far-from-…