[HTML][HTML] Chordal and factor-width decompositions for scalable semidefinite and polynomial optimization

Y Zheng, G Fantuzzi, A Papachristodoulou - Annual Reviews in Control, 2021‏ - Elsevier
Chordal and factor-width decomposition methods for semidefinite programming and
polynomial optimization have recently enabled the analysis and control of large-scale linear …

Auxiliary functions as Koopman observables: Data-driven analysis of dynamical systems via polynomial optimization

JJ Bramburger, G Fantuzzi - Journal of Nonlinear Science, 2024‏ - Springer
We present a flexible data-driven method for dynamical system analysis that does not
require explicit model discovery. The method is rooted in well-established techniques for …

Bounding extreme events in nonlinear dynamics using convex optimization

G Fantuzzi, D Goluskin - SIAM journal on applied dynamical systems, 2020‏ - SIAM
We study a convex optimization framework for bounding extreme events in nonlinear
dynamical systems governed by ordinary or partial differential equations (ODEs or PDEs) …

Convergence of Lasserre's hierarchy: the general case

M Tacchi - Optimization Letters, 2022‏ - Springer
Lasserre's moment-SOS hierarchy consists in approximating instances of the generalized
moment problem (GMP) with moment relaxations and sums-of-squares (SOS) …

Exploiting term sparsity in moment-sos hierarchy for dynamical systems

J Wang, C Schlosser, M Korda… - IEEE Transactions on …, 2023‏ - ieeexplore.ieee.org
In this article, we develop a dynamical system counterpart to the term sparsity sum-of-
squares algorithm proposed for static polynomial optimization. This allows for computational …

Encoding inductive invariants as barrier certificates: Synthesis via difference-of-convex programming

Q Wang, M Chen, B Xue, N Zhan, JP Katoen - Information and Computation, 2022‏ - Elsevier
We present the invariant barrier-certificate condition that witnesses unbounded-time safety
of differential dynamical systems. The proposed condition is the weakest possible one to …

Converging outer approximations to global attractors using semidefinite programming

C Schlosser, M Korda - Automatica, 2021‏ - Elsevier
This paper develops a method for obtaining guaranteed outer approximations for global
attractors of continuous and discrete time nonlinear dynamical systems. The method is …

Peak estimation for uncertain and switched systems

J Miller, D Henrion, M Sznaier… - 2021 60th IEEE …, 2021‏ - ieeexplore.ieee.org
Peak estimation bounds extreme values of a function of state along trajectories of a
dynamical system. This paper focuses on extending peak estimation to continuous and …

[ספר][B] Data-Driven Methods for Dynamic Systems

JJ Bramburger - 2024‏ - SIAM
Excerpt This book grew out of multiple stimulating conversations with Nathan Kutz while I
was a postdoc at the University of Washington. It began with joking about taking our favorite …

Moment-SOS hierarchy for large scale set approximation. Application to power systems transient stability analysis

M Tacchi - 2021‏ - laas.hal.science
This thesis deals with approximating sets using Lasserre's moment-SOS hierarchy. The
motivation is the increasing need for efficient methods to approximate sets of secure …