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Karthik Elamvazhuthi @clopenloop.bsky.social · 26/09/2026

Blogposts compiled as Some working notes on generative modeling feedback control and Planning. Alternative titles include "Control as Transport" "A Measure Theoretic view of Control" Link: tinyurl.com/35jxd2tt

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Karthik Elamvazhuthi @clopenloop.bsky.social · 03/09/2026

This week in clopenloop we look at the the ergodic control problem. Rather than stabilizing a system to a point, can we make a single trajectory spend the right fraction of time across space? Maybe instead of engineering stability, we want chaos. hackmd.io/@clopenloop/...

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Karthik Elamvazhuthi @clopenloop.bsky.social · 08/08/2026

For problems like system identification and RL, sampling from the reachable set is important. Many works deal with the discrete time case for sampling. The corresponding sampling strategy for continuous time catastrophically fail: "How not to sample from the reachable set" tinyurl.com/4r6fum2m

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Karthik Elamvazhuthi @clopenloop.bsky.social · 12/07/2026

The proximal point scheme can be seen as a MPC like iteration for the single integrator. So naturally, there should be a similar optimal control scheme for the heavy ball dynamics using the double integrator. Blog post: hackmd.io/@clopenloop/...

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Karthik Elamvazhuthi @clopenloop.bsky.social · 03/07/2026

The sub-Laplacian encodes information about a control system's geometry. One can use linear Poisson equation to design controllers for nonlinear control systems. An interesting connection between linear PDE tools and geometric control. Link to post: hackmd.io/@clopenloop/...

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Karthik Elamvazhuthi @clopenloop.bsky.social · 22/06/2026

It is standard to view control of multi-agent systems or swarms are special cases of classical control problems. But in the measure viewpoint, classical control problems are special cases of the swarm problem. Latest post: hackmd.io/@clopenloop/...

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Karthik Elamvazhuthi @clopenloop.bsky.social · 07/06/2026

Blogpost on how the maximum principle of optimal control and the corresponding Hamiltonian system can be integrated with flow matching to develop a regression based approach to control synthesis, and a comparison with an elementary model based policy gradient method. hackmd.io/@clopenloop/...

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Karthik Elamvazhuthi @clopenloop.bsky.social · 22/05/2026

Continuing with the line thinking that topological obstructions to smooth stabilization can be avoided by adding noise. All a simple consequence of an eerie observation of Khasʹminskiĭ's that global recurrence plus local stability gives asymptotic stability. Preprint: tinyurl.com/mth23ux4

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Karthik Elamvazhuthi @clopenloop.bsky.social · 20/05/2026

One does not need white noise to implement the principle of denoising diffusion. For instance, RRT* from robotics is a more efficient way to explore the space than Brownian motion. One can combine this with flow matching to denoise the system to construct feedback navigating control laws.

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Karthik Elamvazhuthi @clopenloop.bsky.social · 18/05/2026

If one starts with a reference ergodic process, and composes it with a transport map, then you get a new process ergodic with respect to the terminal transported measure.

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Karthik Elamvazhuthi @clopenloop.bsky.social · 08/05/2026

Not quite ready to compete with a diffusion model. But getting there

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Karthik Elamvazhuthi @clopenloop.bsky.social · 06/05/2026

Hooked up a hand gesture system with a swarm of interaction particles, leading to a notion of “Swarm bending” Motivates interesting theoretical questions regarding which swarm models are “bendable.” hackmd.io/@clopenloop/...

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Karthik Elamvazhuthi @clopenloop.bsky.social · 06/05/2026

Bahaha Source: michaellevitin.net/Book/TSG2305...

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Karthik Elamvazhuthi @clopenloop.bsky.social · 04/05/2026

Forget proofs. I want to learn to make falling cats like these. Source: Lecture notes on sub-Riemannian geometry from the Lie group viewpoint - Enrico Le Donne cvgmt.sns.it/media/doc/pa...

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Karthik Elamvazhuthi @clopenloop.bsky.social · 17/04/2026

Bees on the 2D simplex. Which simplex do we choose?

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Karthik Elamvazhuthi @clopenloop.bsky.social · 16/04/2026

Round 2 of collective decision making as a feedback control problem. This time we visit the Seeley model. How do bees avoid deadlock and obstructions to stabilization? To control engineers need to practice headbutting? hackmd.io/yTBuClZ0Sh65...

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Karthik Elamvazhuthi @clopenloop.bsky.social · 08/04/2026

Latest blog post of clopenloop is coincidentally on how the generative modeling method of flow matching can be used to go from open loop trajectories to closed loop based feedback synthesis. t.co/q0InluvTWy

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Karthik Elamvazhuthi @clopenloop.bsky.social · 29/03/2026

The inverted pendulum is steered to its Sisyphean headstand once more. But without eigenvalues, Lyapunov, or bribery. Instead, using denoising as a control steering mechanism. Latest post on generative modeling for control: hackmd.io/kjV3PiI4ROOP...

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Karthik Elamvazhuthi @clopenloop.bsky.social · 28/03/2026

The Fall from the Ivory Tree An essay on the despair of the academic job cycle, and the hope that must follow - hackmd.io/@clopenloop/...

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Karthik Elamvazhuthi @clopenloop.bsky.social · 03/02/2026

Encoding geometry in neural network architectures has wide applications, from robots' configuration spaces to safety. We present natural ways to enforce constraints by design. Link to preprint: www.researchgate.net/publication/... #geometricdeeplearning

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Karthik Elamvazhuthi @clopenloop.bsky.social · 24/11/2025

I’m writing notes on how generative modeling connects with control theory. Starting with intuition: simulations, nonlinear control, and how stochastic dynamics can shape long-term behavior. LN1 (Fokker–Planck): hackmd.io/@clopenloop/... LN2 (Nonholonomic Fokker-Planck): hackmd.io/@clopenloop/...

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Karthik Elamvazhuthi @clopenloop.bsky.social · 31/10/2025

The road to the maximum principle turns out to be more non-smooth than one might expect. Boltyanski, Martini & Soltan’s book ( Geometric Methods and Optimization Problems) has far more drama than you’d guess from the Sussmann–Willems survey.

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Karthik Elamvazhuthi @clopenloop.bsky.social · 24/10/2025

Job season in academia can take a toll on confidence, identity, and energy. You’re not alone. Sometimes it helps to zoom out. Hunter Wapman’s thesis highlights some interesting hiring patterns: www.hne.golf/static/pdfs/... Non-US trends may differ, perhaps shaping distinct knowledge bubbles.

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Karthik Elamvazhuthi @clopenloop.bsky.social · 21/09/2025

Naive random sampling of initial conditions and control.

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Karthik Elamvazhuthi @clopenloop.bsky.social · 21/09/2025

Optimal Transport (OT) is emerging as a versatile tool for control questions. We show an OT-based way to sample from the reachable set (RS), especially useful when systems have strong attractors. www.researchgate.net/publication/... RS of Van der Pol vs. naive random sampling (below).

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Karthik Elamvazhuthi @clopenloop.bsky.social · 30/06/2025

I am starting to compile some notes on Generative Modeling for Control Theory. The goal is to include topics such as degenerate Fokker-Planck equations (FPEs) and Optimal transport theory. Here is a first post on the classical (nicer) FPE and its long-term behavior. hackmd.io/@clopenloop/...

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Karthik Elamvazhuthi @clopenloop.bsky.social · 05/06/2025

Probably a good chapter if it starts with Nietzsche. - Tanja Eisner, Bálint Farkas, Markus Haase and Rainer Nagel (Operator Theoretic Aspects of Ergodic Theory)

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Karthik Elamvazhuthi @clopenloop.bsky.social · 14/04/2025

Denoising an unstable double integrator to sum of two Dirac measures. See details on the theory in the preprint: www.researchgate.net/publication/... #controltheory #machinelearning #diffusionmodels bsky.app/profile/clop...

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Karthik Elamvazhuthi @clopenloop.bsky.social · 06/04/2025

A blog post on how diffusion models can be used for planning in domains with obstacles : hackmd.io/@TAzH1D5uSQO...

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Karthik Elamvazhuthi @clopenloop.bsky.social · 15/12/2024

Convexity lies in the eye of beholder. A note on how nonlinear optimal control problems can be given a convex formulation using the continuity equation. hackmd.io/@TAzH1D5uSQO... #controltheory

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Karthik Elamvazhuthi @clopenloop.bsky.social · 14/12/2024

Switching between two flows of a skinny neural ODE (blue and red) produces the behavior of a time-averaged thick neural ODE (green).

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