Related papers: Characterizing Safety: Minimal Barrier Functions f…
Modern nonlinear control theory seeks to endow systems with properties of stability and safety, and have been deployed successfully in multiple domains. Despite this success, model uncertainty remains a significant challenge in synthesizing…
This book deals with functions allowing to express the dissimilarity (discrepancy) between two data fields or ''divergence functions'' with the aim of applications to linear inverse problems. Most of the divergences found in the litterature…
This is the first of a series of papers devoted to a thorough analysis of the class of gradient flows in a metric space $(X,\mathsf{d})$ that can be characterized by Evolution Variational Inequalities. We present new results concerning the…
We show that the graph of a bent function is a Salem set in an appropriate sense. We also establish a simple result that quantifies redundancies in the difference operators of a function, which applies to bent functions over fields of odd…
When studying fluid mechanics in terms of instability, bifurcation and invariant solutions one quickly finds out how little can be done by pen and paper. For flows on sufficiently simple domains and under sufficiently simple boundary…
We study distribution-free predictive inference for data with group symmetries, aiming to establish near-conditional coverage guarantees beyond exchangeability for structured data. While many predictive inference methods achieve a target…
In this paper, we are concerned with the sign-changing solutions of variational inequality problems. In order to give the existence results of the sign-changing solutions for variational inequality problems, we first construct a suitable…
A common assumption on the deployment of safeguarding controllers on the digital platform is that high sampling frequency translates to a small violation of safety. This paper investigates and formalizes this assumption through the lens of…
This paper introduces integral control barrier functions (I-CBFs) as a means to enable the safety-critical integral control of nonlinear systems. Importantly, I-CBFs allow for the holistic encoding of both state constraints and input bounds…
Certifying power flow solvability is important for reliable power system operations under volatile operating conditions, but solving power flow equations repeatedly can be costly and may encounter convergence issues. In this paper, we…
Systems biology relies on mathematical models that often involve complex and intractable likelihood functions, posing challenges for efficient inference and model selection. Generative models, such as normalizing flows, have shown…
We consider perturbations of unitary minimal models by boundary fields. Initially we consider the models in the limit as c -> 1 and find that the relevant boundary fields all have simple interpretations in this limit. This interpretation…
We present an approach to the verification of systems for whose description some elements - constants or functions - are underspecified and can be regarded as parameters, and, in particular, describe a method for automatically generating…
This is the second in a series of articles aimed at exploring the relationship between the complexity classes of P and NP. The research in this article aims to find conditions of an algorithmic nature that are necessary and sufficient to…
In this paper, we consider functionals of the form $H_\alpha(u)=F(u)+\alpha G(u)$ with $\alpha\in[0,+\infty)$, where $u$ varies in a set $U\neq\emptyset$ (without further structure). We first revisit a result stating that, excluding at most…
We deal with finite dimensional linear and nonlinear control systems. If the system is linear and autonomous and satisfies the classical normality assumption, we improve the well known result on the strict convexity of the reachable set…
In this paper, vector optimization is considered in the framework of decision making and optimization in general spaces. Interdependencies between domination structures in decision making and domination sets in vector optimization are…
Functions of one or more variables are usually approximated with a basis: a complete, linearly-independent system of functions that spans a suitable function space. The topic of this paper is the numerical approximation of functions using…
Control Barrier Functions (CBFs) have become a popular tool for enforcing set invariance in safety-critical control systems. While guaranteeing safety, most CBF approaches are myopic in the sense that they solve an optimization problem at…
This paper presents a methodology for ensuring that the composition of multiple Control Barrier Functions (CBFs) always leads to feasible conditions on the control input, even in the presence of input constraints. In the case of a system…