A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Study of control problems on Carnot groups with SO(3) symmetry using geometric algebra.
Introduces geometric control theory for students.
Enhances quantum circuit synthesis using deep learning and geometric methods.
Survey of recent developments in symmetric reductions and controls for Hamiltonian systems.
We use the methods of geometric control theory to study extremal trajectories of vertical rolling disk. We focus on the role of symmetries of the underlying geometric structures. We demonstrate the computations in the CAS Maple package DifferentialGeometry.
Survey explores geometric aspects of policy optimization in control systems.
In this paper we present a geometric control law for position and line-of-sight stabilization of the nonholonomic spherical robot actuated by three independent actuators. A simple configuration error function with an appropriately defined transport map is proposed to extract feedforward and proportional-derivative cont…
Study of 2D Lorentzian anti-de Sitter plane using geometric control theory.
Hybrid systems are characterized by having an interaction between continuous dynamics and discrete events. The contribution of this paper is to provide hybrid systems with a novel geometric formulation so that controls can be added. Using this framework we describe some new global controllability tests for hybrid contr…
Geometric framework for dynamic feedback linearization of control systems with symmetry.
We geometrically describe optimal control problems in terms of Morse families in the Hamiltonian framework. These geometric structures allow us to recover the classical first order necessary conditions for optimality and the starting point to run an integrability algorithm. Moreover the integrability algorithm is adapt…
New geometric approach controls motion of a spinning sphere on a plane.
In this paper, from the viewpoint of completeness of Marsden-Weinstein reduction, we illustrate how to give the definitions of a controlled Hamiltonian (CH) system and a reducible controlled Hamiltonian system with symmetry; and how to describe the dynamics of a CH system and the controlled Hamiltonian equivalence; as …
New approach to control diffusion processes with soft constraints.
Just as an explicit parameterisation of system dynamics by state, i.e., a choice of coordinates, can impede the identification of general structure, so it is too with an explicit parameterisation of system dynamics by control. However, such explicit and fixed parameterisation by control is commonplace in control theory…
We use neural networks as control variates with geometric integration techniques.
New measure shows various training techniques control model complexity.
Geometric methods integrate Lie systems for optimal control problems.
Study optimal paths in Zermelo's navigation problem using geometric equations.
Introduces GFC for learning complex dynamical systems with geometric constraints.
The symmetric product of vector fields on a manifold arises when one studies the controllability of certain classes of mechanical control systems. A geometric description of the symmetric product is provided using parallel transport, along the lines of the flow interpretation of the Lie bracket. This geometric interpre…
Optimal tracking of nonholonomic systems using geometric methods.
We study local control of the mechanism with the growth vector (4,7). We study controllability and extremal trajectories on the nilpotent approximation as an example of the control theory on Lie group. We give solutions of the system an show examples of local extremal trajectories.
The purpose of this paper is to use the framework of Lie algebroids to study optimal control problems for affine connection control systems on Lie groups. In this context, the equations for critical trajectories of the problem are geometrically characterized as a Hamiltonian vector field.
A close relationship between the classical Hamilton-Jacobi theory and the kinematic reduction of control systems by decoupling vector fields is shown in this paper. The geometric interpretation of this relationship relies on new mathematical techniques for mechanics defined on a skew-symmetric algebroid. This geometric…
Motion planning and control are key problems in a collection of robotic applications including the design of autonomous agile vehicles and of minimalist manipulators. These problems can be accurately formalized within the language of affine connections and of geometric control theory. In this paper we overview recent r…
Geometric stability predicts steerability and detects drift in language models.
Algorithm reduces control regret for unknown systems.
Randomized control methods improve asset pricing and performance analysis.
Paper studies optimal control for a specific geometric problem.
Paper proposes a closed-form formula for geometric Istanbul call options.
The paper compares numerical schemes for nonholonomic systems using retraction maps.
In this paper, we first give the regular point reduction and the two types of Hamilton-Jacobi equation for a regular controlled Hamiltonian (RCH) system with symmetry and momentum map on the generalization of a semidirect product Lie group. Next, as an application of the theoretical results, we consider the underwater …
In this paper, we consider the asset-liability management under the mean-variance criterion. The financial market consists of a risk-free bond and a stock whose price process is modeled by a geometric Brownian motion. The liability of the investor is uncontrollable and is modeled by another geometric Brownian motion. W…
Geometrically characterizes virtual nonlinear nonholonomic constraints using symplectic methods.
Introduces optimization geometrodynamics for dynamic geometric optimization.
We show an example providing a significance in geometric control theory of the existence of the dependence locus of a system of vector fields in particular, the generic appearance of non-trivial singular trajectories embedded in the dependence locus.
Geometric framework explains and controls implicit bias in machine learning.
We discuss some challenging open problems in the geometric control theory and sub-Riemannian geometry.
New method uses geometric mean to avoid non-collapsibility in case-control studies.
Unified geometric formulation of Maxwell-Vlasov system using presymplectic and symmetry reduction.
In this paper long-run risk sensitive optimisation problem is studied with dyadic impulse control applied to continuous-time Feller-Markov process. In contrast to the existing literature, focus is put on unbounded and non-uniformly ergodic case by adapting the weight norm approach. In particular, it is shown how to com…
In this paper, we describe a geometric setting for higher-order lagrangian problems on Lie groups. Using left-trivialization of the higher-order tangent bundle of a Lie group and an adaptation of the classical Skinner-Rusk formalism, we deduce an intrinsic framework for this type of dynamical systems. Interesting appli…
The paper extends a geometric model using singular curves.
The aim of this paper is to adapt the general multitime maximum principle to a Riemannian setting. More precisely, we intend to study geometric optimal control problems constrained by the metric compatibility evolution PDE system; the evolution ("multitime") variables are the local coordinates on a Riemannian manifold,…
This article presents some methods to control the bottom of the spectrum of the Laplacian on hyperbolic surfaces with infinite volume. Our first result bounds the of a geometrically finite surface in terms of the geometry of its convex core. We then focus on infinite type periodic hyperbolic surfaces built …
We explain the geometric origin of the -algebra controlling deformations of pre-symplectic structures.
Study shows observability for Schrödinger equations on product manifolds with specific conditions.