Karthik Elamvazhuthi

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: @clopenloop/H1qbN4d6We" target="_blank" rel="nofollow noopener">hackmd.io/@clopenloop/H1…

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: @clopenloop/BJ2vLuH7Ge" target="_blank" rel="nofollow noopener">hackmd.io/@clopenloop/BJ…

@canonical777 As far as I know he doesn’t do numerical PDEs. Maybe he can learn on the job.

@clopenloop Lmao this is actually real, congratulations to Terence Tao on being the only qualified candidate for the Terence Tao role

The job market is crazy these days.

@PiyushGrover101 My theory is we will all become the ETH Professor with a lab of 20plus PhD students, who has no clue what’s going on in their own research. We are all currently in our early career phase, where we are able to guide the students in the best directions.

If AI can (enventually) handle all the messy details in math, will that mean we will all become diagram chasers ?

The Hamiltonian system from optimal control can be used to noise-denoise control systems. Gives deterministic alternative to injecting noise through controls for feedback control. Comparison with an elementary model based policy gradient method included. @clopenloop/H1yt3Ty-Ge" target="_blank" rel="nofollow noopener">hackmd.io/@clopenloop/H1…

Topological obstructions to smooth global stabilization can be avoided by adding noise. Also, one can globally converge to minimizer of strongly convex function in domain with non-convex constraints. Preprint: tinyurl.com/mth23ux4 #controltheory #optimization

Start with a reference ergodic process, and compose it with a transport map. You get a new process ergodic with respect to the terminal transported measure. An easy way to stabilize systems to a target ergodic objective. Another alternative: R o T o inv(R)

🥇 Congrats to Arthur J. Krener — winner of the IFAC Giorgio Quazza Medal 2023–2026! For fundamental contributions to nonlinear systems analysis, estimation, control & optimization. 50+ years shaping the field. To be honored at #IFAC2026 in Busan. 📄 buff.ly/E6AmEAn

Repulsive leaders have poorer controllability: duh (Limitations of the study: repulsive leaders are four of my fingers.) Splitting by two charismatic charmers on the other hand. #SwarmBending #HumanSwarmInteraction

This week, the bees have elevated in their collective decision making dynamics, from Euclidean gradient flows to Wasserstein gradient flows. As higher beings they have to now confront a more complex equilibria landscape. @clopenloop/rkftIi6Tbe" target="_blank" rel="nofollow noopener">hackmd.io/@clopenloop/rk…

Before I get into the heart of the presentation, I would like to thank my two amazingly talented students who lead all of this work, ChatGPT browser tab 2 and Claude browser tab 3. #fundingcuts #academia

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? Do control engineers need to practice headbutting? hackmd.io/yTBuClZ0Sh65Pz… #controltheory

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. Link: @clopenloop/HkVqN0ZnWx" target="_blank" rel="nofollow noopener">hackmd.io/@clopenloop/Hk… #controltheory #flowmatching #machinelearning

New lecture in a series on Generative Modeling for Control problems. We see how denoising diffusion based feedback control specializes to control affine systems with drift. Link: hackmd.io/kjV3PiI4ROOPb_… #diffusionmodels #controltheory

New lecture in a series on Generative Modeling for Control problems. We see how denoising diffusion based feedback control specializes to Linear Time Invariant Systems (LTIs). Link: tinyurl.com/bde872ez For other lectures: sites.google.com/view/karthikel… #controltheory #diffusion

Link to my zoom talk at the GERAD Research Center, "A Transport Theoretic Perspective for Nonlinear Control": youtube.com/watch?v=cXy1mj… Thanks to the organizers, Aditya Mahajan, Peter Caines, and Shuang Gao for the nice interactive session. #Controltheory

New lecture in a series on Generative Modeling for Control problems. I introduce a control version of gradient descent: The nonholonomic gradient descent. hackmd.io/pTtk6ohHSBSfqL… For other lectures: sites.google.com/view/karthikel… #Controltheory #generativemodeling

Encoding geometry in neural network architectures has wide applications, from robots' configuration spaces to safety. With @RishiSonthalia, we present and compare differential geometric and variational ways to enforce constraints by design. Preprint: tinyurl.com/38zkkars

@beenwrekt A different connection inspiring a nonlinear control framework using the optimization analogy is going from gradient descent to gradient descent along restricted control directions.

With analogies to optimization algorithms, I describe a path to generalize from linear to nonlinear control. argmin.net/p/sweet-spots-…