13 citations · 34 across the 28 of their papers we have counts for
15 papers · 1 filter
Noise-Induced Navigation in Non-convex Domains and Compact Manifolds
Karthik Elamvazhuthi
In this note, we study the problem of designing a feedback law that globally steers a system to a prescribed target configuration. Even if the system is fully actuated, topological…
Notes on Generative Modeling for Feedback Control and Planning
Karthik Elamvazhuthi
In these notes, we view control as a dynamically constrained sampling problem on the state-space of a control system. With this viewpoint, we extend methods from generative modelin…
From Schrodinger Bridge to Optimal Transport over Sub-Riemannian Manifolds
Daniel Owusu Adu, Karthik Elamvazhuthi, Bahman Gharesifard
We study the least-energy way to reshape a probability distribution when motion is constrained to a horizontal bundle, that is, optimal transport and distribution steering in sub-R…
Flow Matching for Measure Transport and Feedback Stabilization of Control-Affine Systems
Karthik Elamvazhuthi
We develop a \emph{flow-matching framework} for transporting probability measures under control-affine dynamics and for steering systems to points or target sets. Starting from the…
Uniform Sampling from the Reachable Set Using Optimal Transport
Karthik Elamvazhuthi, Sachin Shivakumar
Estimating the reachable set of a dynamical system is a fundamental problem in control theory, particularly when control inputs are bounded. Direct simulation using randomly sample…
Score Matching Diffusion Based Feedback Control and Planning of Nonlinear Systems
Karthik Elamvazhuthi, Darshan Gadginmath, Fabio Pasqualetti
In this paper, we propose a deterministic diffusion-based framework for controlling the probability density of nonlinear control-affine systems, with theoretical guarantees for dri…
The Ground Cost for Optimal Transport of Angular Velocity
Karthik Elamvazhuthi, Abhishek Halder
We revisit the optimal transport problem over angular velocity dynamics given by the controlled Euler equation. The solution of this problem enables stochastic guidance of spin sta…
Quantitative Flow Approximation Properties of Narrow Neural ODEs
Karthik Elamvazhuthi
In this note, we revisit the problem of flow approximation properties of neural ordinary differential equations (NODEs). The approximation properties have been considered as a flow…
Benamou-Brenier Formulation of Optimal Transport for Nonlinear Control Systems on Rd
Karthik Elamvazhuthi
In this paper we consider the Benamou-Brenier formulation of optimal transport for nonlinear control affine systems on $\Rd$, removing the compactness assumption of the underlying…
A Linear Test for Global Nonlinear Controllability
Karthik Elamvazhuthi
It is known that if a nonlinear control affine system without drift is bracket generating, then its associated sub-Laplacian is invertible under some conditions on the domain. In t…
A Blob Method for Mean Field Control With Terminal Constraints
Katy Craig, Karthik Elamvazhuthi, Harlin Lee
In the present work, we develop a novel particle method for a general class of mean field control problems, with source and terminal constraints. Specific examples of the problems…
Denoising Diffusion-Based Control of Nonlinear Systems
Karthik Elamvazhuthi, Darshan Gadginmath, Fabio Pasqualetti
We propose a novel approach based on Denoising Diffusion Probabilistic Models (DDPMs) to control nonlinear dynamical systems. DDPMs are the state-of-art of generative models that h…
Optimal Transport of Linear Systems over Equilibrium Measures
Karthik Elamvazhuthi, Matt Jacobs
We consider the optimal transport problem over convex costs arising from optimal control of linear time-invariant(LTI) systems when the initial and target measures are assumed to b…
Learning on Manifolds: Universal Approximations Properties using Geometric Controllability Conditions for Neural ODEs
Karthik Elamvazhuthi, Xuechen Zhang, Samet Oymak +1
In numerous robotics and mechanical engineering applications, among others, data is often constrained on smooth manifolds due to the presence of rotational degrees of freedom. Comm…
Neural ODE Control for Trajectory Approximation of Continuity Equation
Karthik Elamvazhuthi, Bahman Gharesifard, Andrea Bertozzi +1
We consider the controllability problem for the continuity equation, corresponding to neural ordinary differential equations (ODEs), which describes how a probability measure is pu…