Naive random sampling of initial conditions and control.

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).

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/...

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...

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

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

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