Chordal and factor-width decomposition methods for semidefinite programming and
polynomial optimization have recently enabled the analysis and control of large-scale linear …

This work proposes a new moment-SOS hierarchy, called CS-TSSOS, for solving large-
scale sparse polynomial optimization problems. Its novelty is to exploit simultaneously …

In this paper we prove general sparse decomposition of dynamical systems provided that
the vector field and constraint set possess certain structures, which we call subsystems. This …

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 …

This paper develops a method for obtaining guaranteed outer approximations for global
attractors of continuous and discrete time nonlinear dynamical systems. The method is …

This paper focuses on the computation of joint spectral radii (JSR), when the involved
matrices are sparse. We provide a sparse variant of the procedure proposed by Parrilo and …

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 …

Online control design using a high-fidelity, full-order model for a bipedal robot can be
challenging due to the size of the state space of the model. A commonly adopted solution to …

While stability analysis is a mainstay for control science, especially computing regions of
attraction of equilibrium points, until recently most stability analysis tools always required …

We introduce a sublevel Moment-SOS hierarchy where each SDP relaxation can be viewed
as an intermediate (or interpolation) between the d-th and (d+ 1)(d+ 1)-th order SDP …