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We consider the long-term evolution of an inhomogeneous long-range interacting $N$-body system. Placing ourselves in the dynamically hot limit, i.e. neglecting collective effects, we derive a large deviation principle for the system's…
Energetic particle effects in magnetic confinement fusion devices are commonly studied by hybrid kinetic-fluid simulation codes whose underlying continuum evolution equations often lack the correct energy balance. While two different…
We consider the assimilation of Lagrangian data into a primitive equations circulation model of the ocean at basin scale. The Lagrangian data are positions of floats drifting at fixed depth. We aim at reconstructing the four-dimensional…
A class of variational schemes for the hydrodynamic-electrodynamic model of lossless free-electron gas in a quasineutral background is developed for high-quality simulations of surface plasmon polaritons. The Lagrangian density of lossless…
We present a differentiable dynamics solver that is able to handle frictional contact for rigid and deformable objects within a unified framework. Through a principled mollification of normal and tangential contact forces, our method…
We prove pathwise large deviation principles of slow variables in slow-fast systems in the limit of time-scale separation tending to infinity. In the limit regime we consider, the convergence of the slow variable to its deterministic limit…
Incorporating prior knowledge of physics laws and structural properties of dynamical systems into the design of deep learning architectures has proven to be a powerful technique for improving their computational efficiency and…
We study the problem of motion feasibility for multiagent control systems on Lie groups with collision avoidance constraints. We first consider the problem for kinematic left invariant control systems and next, for dynamical control systems…
We propose a novel algorithmic method for constructing invariant variational schemes of systems of ordinary differential equations that are the Euler-Lagrange equations of a variational principle. The method is based on the invariantization…
A variational formulation of accelerated optimization on normed spaces was recently introduced by considering a specific family of time-dependent Bregman Lagrangian and Hamiltonian systems whose corresponding trajectories converge to the…
This paper proposes D-ripALM, a Decentralized relative-type inexact proximal Augmented Lagrangian Method for consensus convex optimization over multi-agent networks. D-ripALM adopts a double-loop distributed optimization framework that…
Aerial manipulators (AM) exhibit particularly challenging, non-linear dynamics; the UAV and the manipulator it is carrying form a tightly coupled dynamic system, mutually impacting each other. The mathematical model describing these…
This work is devoted to a systematic exposition of the dynamics of a rigid body, considered as a system with kinematic constraints. Having accepted the variational problem in accordance with this, we no longer need any additional postulates…
A multi-agent optimization problem motivated by the management of energy systems is discussed. The associated cost function is separable and convex although not necessarily strongly convex and there exist edge-based coupling equality…
A scheme for generating a family of convex variational principles is developed, the Euler- Lagrange equations of each member of the family formally corresponding to the necessary conditions of optimal control of a given system of ordinary…
In this paper, we present two Hermite polynomial based approaches to derive one-step numerical integrators for mechanical systems. These methods are based on discretizing the configuration using Hermite polynomials which leads to numerical…
Systems subjected to holonomic constraints follow quite complicated dynamics that could not be described easily with Hamiltonian or Lagrangian dynamics. The influence of holonomic constraints in equations of motions is taken into account by…
Controlled Lagrangian and matching techniques are developed for the stabilization of relative equilibria and equilibria of discrete mechanical systems with symmetry as well as broken symmetry. Interesting new phenomena arise in the…
An iterative optimization approach that simultaneously minimizes the energy and optimizes the Lagrange multipliers enforcing desired constraints is presented. The method is tested on previously established benchmark systems and it is proved…
The flocking motion control is concerned with managing the possible conflicts between local and team objectives of multi-agent systems. The overall control process guides the agents while monitoring the flock-cohesiveness and localization.…