Related papers: A Comparison Between Lie Group- and Lie Algebra- B…
Contraction theory formulates the analysis of nonlinear systems in terms of Jacobian matrices. Although this provides the potential to develop a linear matrix inequality (LMI) framework for nonlinear control design, conditions are imposed…
We give a brief introduction to Hamiltonian optics and Lie algebraic methods. We use these methods to describe the operators governing light propagation, refraction and reflection in phase space. The method offers a systematic way to find…
Self-interaction error (SIE), arising from the imperfect cancellation of the spurious classical Coulomb interaction between an electron and itself, is a persistent challenge in modern density functional approximations. This issue is…
Series elastic actuators (SEA) were introduced for serial robotic arms. Their model-based trajectory tracking control requires the second time derivatives of the inverse dynamics solution, for which algorithms were proposed. Trajectory…
This paper considers the integration of rigid cooperative manipulation with rigidity theory. Motivated by rigid models of cooperative manipulation systems, i.e., where the grasping contacts are rigid, we introduce first the notion of…
Since they were introduced in the 1990s, Lie group integrators have become a method of choice in many application areas. These include multibody dynamics, shape analysis, data science, image registration and biophysical simulations. Two…
Motivated by the problem of formation control for vehicles moving at unit speed in three-dimensional space, we are led to models of gyroscopically interacting particles, which require the machinery of curves and frames to describe and…
We propose a notion of distance between two parametrized planar curves, called their discrepancy, and defined intuitively as the minimal amount of deformation needed to deform the source curve into the target curve. A precise definition of…
In this paper we study, from a variational and geometrical point of view, second-order variational problems on Lie groupoids and the construction of variational integrators for optimal control problems. First, we develop variational…
In this paper, we describe several different meanings for the concept of Gibbs measure on the lattice $\mathbb{N}$ in the context of finite alphabets (or state space). We compare and analyze these "in principle" distinct notions: DLR-Gibbs…
Offline Reinforcement Learning (RL) promises the recovery of optimal policies from static datasets, yet it remains susceptible to the overestimation of out-of-distribution (OOD) actions, particularly in fractured and sparse data manifolds.…
For over fifty years, the dynamical systems perspective has had a prominent role in evolutionary biology and economics, through the lens of game theory. In particular, the study of replicator differential equations on the standard…
We investigate a Geometric Brownian Information Engine (GBIE) in the presence of an error-free feedback controller that transforms the information gathered on the state of Brownian particles entrapped in monolobal geometric confinement into…
Classical mechanical systems are defined by their kinetic and potential energies. They generate a Lie algebra under the canonical Poisson bracket. This Lie algebra, which is usually infinite dimensional, is useful in analyzing the system,…
We study in this paper the infinite-dimensional orthogonal Lie algebra $\mathcal{O}_C$ which consists of all bounded linear operators $T$ on a separable, infinite-dimensional, complex Hilbert space $\mathcal{H}$ satisfying $CTC=-T^*$, where…
This paper is a contribution to the study of the relations between special functions, Lie algebras and rigged Hilbert spaces. The discrete indices and continuous variables of special functions are in correspondence with the representations…
Iterative Learning Control (ILC) can achieve perfect tracking performance for mechatronic systems. The aim of this paper is to present an ILC design tutorial for industrial mechatronic systems. First, a preliminary analysis reveals the…
In real-world robotics applications, accurate models of robot dynamics are critical for safe and stable control in rapidly changing operational conditions. This motivates the use of machine learning techniques to approximate robot dynamics…
Integrated sensing and communications (ISAC) is an essential technology for the 6G communication system, which enables the conventional wireless communication network capable of sensing targets around. The shared use of pilots is a…
Grid-forming (GFM) inverter-based resources (IBRs) can emulate the external characteristics of synchronous generators (SGs) through appropriate control loop design. However, in systems with GFM IBRs, the apparent impedance trajectory under…