[HTML][HTML] Chordal and factor-width decompositions for scalable semidefinite and polynomial optimization
Chordal and factor-width decomposition methods for semidefinite programming and
polynomial optimization have recently enabled the analysis and control of large-scale linear …
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
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 …
require explicit model discovery. The method is rooted in well-established techniques for …
Bounding extreme events in nonlinear dynamics using convex optimization
We study a convex optimization framework for bounding extreme events in nonlinear
dynamical systems governed by ordinary or partial differential equations (ODEs or PDEs) …
dynamical systems governed by ordinary or partial differential equations (ODEs or PDEs) …
Convergence of Lasserre's hierarchy: the general case
Lasserre's moment-SOS hierarchy consists in approximating instances of the generalized
moment problem (GMP) with moment relaxations and sums-of-squares (SOS) …
moment problem (GMP) with moment relaxations and sums-of-squares (SOS) …
Exploiting term sparsity in moment-sos hierarchy for dynamical systems
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 …
squares algorithm proposed for static polynomial optimization. This allows for computational …
Encoding inductive invariants as barrier certificates: Synthesis via difference-of-convex programming
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 …
of differential dynamical systems. The proposed condition is the weakest possible one to …
Converging outer approximations to global attractors using semidefinite programming
This paper develops a method for obtaining guaranteed outer approximations for global
attractors of continuous and discrete time nonlinear dynamical systems. The method is …
attractors of continuous and discrete time nonlinear dynamical systems. The method is …
Peak estimation for uncertain and switched systems
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 …
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 …
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 …
motivation is the increasing need for efficient methods to approximate sets of secure …