Related papers: Universal limit theorem for rough differential equ…
We study a class of controlled rough differential equations. It is shown that the value function satisfies a HJB type equation; we also establish a form of the Pontryagin maximum principle. Deterministic problems of this type arise in the…
Directed sandpile models with different toppling rules are studied by means of numerical simulations in two dimensions, with the purpose of determining the different universality classes. It is concluded that the random-threshold directed…
First order optimization algorithms play a major role in large scale machine learning. A new class of methods, called adaptive algorithms, were recently introduced to adjust iteratively the learning rate for each coordinate. Despite great…
Universal approximation theorems establish the expressive capacity of neural network architectures. For dynamical systems, existing results are limited to finite time horizons or systems with a globally stable equilibrium, leaving…
In line with the notion of probabilistic rough paths introduced in the previous contribution \cite{salkeld2021Probabilistic}, we address corresponding random controlled rough paths (first introduced in \cite{2019arXiv180205882.2B}), the…
In the real-world, self-driving vehicles are required to achieve steering maneuvers in both uncontrolled and uncertain environments while maintaining high levels of safety and passengers' comfort. Ignoring these requirements would…
We derive regularized contour dynamics equations for the motion of infinite sharp fronts in the two-dimensional incompressible Euler, surface quasi-geostrophic (SQG), and generalized surface quasi-geostrophic (gSQG) equations. We derive a…
In this paper, we investigate the problem of coordinated path following for fixed-wing UAVs with speed constraints in 2D plane. The objective is to steer a fleet of UAVs along the path(s) while achieving the desired sequenced inter-UAV arc…
We provide a theory of manifold-valued rough paths of bounded 3 > p-variation, which we do not assume to be geometric. Rough paths are defined in charts, and coordinate-free (but connection-dependent) definitions of the rough integral of…
We use simple sub-Riemannian techniques to prove that an arbitrary geometric p-rough path in the sense of Lyons (98) is the limit in sup-norm of a sequence of canonically lifted smooth paths, which are uniformly bounded in p-variation,…
Deep learning models have gained great success in many real-world applications. However, most existing networks are typically designed in heuristic manners, thus lack of rigorous mathematical principles and derivations. Several recent…
This paper is devoted to the development of adaptive control schemes for uncertain discrete-time systems, which guarantee robust, global, exponential convergence to the desired equilibrium point of the system. The proposed control scheme…
The convergence of the first order Euler scheme and an approximative variant thereof, along with convergence rates, are established for rough differential equations driven by c\`adl\`ag paths satisfying a suitable criterion, namely the…
The averaging principle for slow-fast systems of various kind of stochastic (partial) differential equations has been extensively studied. An analogous result was shown for slow-fast systems of rough differential equations driven by random…
We consider the damped wave equation \alpha u_tt + u_t = u_xx - V'(u) on the whole real line, where V is a bistable potential. This equation has travelling front solutions of the form u(x,t) = h(x-st) which describe a moving interface…
Deep networks have recently been shown to be vulnerable to universal perturbations: there exist very small image-agnostic perturbations that cause most natural images to be misclassified by such classifiers. In this paper, we propose the…
We study the charge transport across a band-tuned metal-insulator transition in two dimensions. For high temperatures $T$ and chemical potentials $\mu$ far from the transition point, conduction is ballistic and the resistance $R(T)$…
There has been substantial recent progress on the theoretical understanding of model-free approaches to Linear Quadratic Regulator (LQR) problems. Much attention has been devoted to the special case when the goal is to drive the state close…
In decentralized control problems, a standard approach is to specify the set of allowable decentralized controllers as a closed subspace of linear operators. This then induces a corresponding set of Youla parameters. Previous work has shown…
The robustness of the universality class concept of the chaotic transition was investigated by analytically obtaining its critical exponent for a wide class of maps. In particular, we extended the existing one-dimensional chaotic maps,…