Motivated by stability analysis of large scale power systems, we describe how the Lasserre
(moment-sums of squares, SOS) hierarchy can be used to generate outer approximations of …

Lasserre's moment-SOS hierarchy consists in approximating instances of the generalized
moment problem (GMP) with moment relaxations and sums-of-squares (SOS) …

We consider the classical problem of invariant generation for programs with polynomial
assignments and focus on synthesizing invariants that are a conjunction of strict polynomial …

We revisit the problem of computing (robust) controlled invariant sets for discrete-time linear
systems. Departing from previous approaches, we consider implicit, rather than explicit …

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 …

Contract theory is a powerful tool to reason on systems that are interacting with an external
environment, possibly made of other systems. Formally, a contract is usually given by …

We introduce a comprehensive framework for analyzing convergence rates for infinite
dimensional linear programming problems (LPs) within the context of the moment-sum-of …

This work presents a data-driven method for approximation of the maximum positively
invariant (MPI) set and the maximum controlled invariant (MCI) set for nonlinear dynamical …

The goal of this paper is to present a systematic method to compute reference dependent
positively invariant sets for systems subject to constraints. To this end, we first characterize …

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 …