Given a network of agents, we say that the agents achieve a k-agreement when their state variables converge to a point that corresponds to the projection of the agents’ states onto …
This work presents a general geometric framework for simulating and learning the dynamics of Hamiltonian systems that are invariant under a Lie group of transformations. This means …
Given a network of agents, we study the problem of designing a distributed algorithm that computes k independent weighted means of the network's initial conditions (namely, the …
In this work we study Beltrami fields with non-constant proportionality factor on $\mathbb{R}^3$. More precisely, we analyze the existence of vector fields $X$ satisfying the …
This paper proposes a data-driven control framework to regulate an unknown, stochastic linear dynamical system to the solution of a (stochastic) convex optimization problem. …
This paper tackles the problem of discretizing accelerated optimization flows while retaining their convergence properties. Inspired by the success of resource-aware control in …
In this paper we develop a geometric version of the Hamilton-Jacobi equation in the Poisson setting. Specifically, we "geometrize" what is usually called a complete solution of the …
Reduction theory has played a major role in the study of Hamiltonian systems. On the other hand, the Hamilton-Jacobi theory is one of the main tools to integrate the dynamics of …
Recently, M. de León el al. ([9]) have developed a geometric Hamilton-Jacobi theory for Classical Field Theories in the setting of multisymplectic geometry. Our purpose in the …
In this paper we develop a Hamilton-Jacobi theory in the setting of almost Poisson manifolds. The theory extends the classical Hamilton-Jacobi theory and can be also applied to …