6 papers
Control-affine Schrödinger Bridge and Generalized Bohm Potential
Alexis M. H. Teter, Abhishek Halder, Michael D. Schneider +4
The control-affine Schrödinger bridge concerns with a stochastic optimal control problem. Its solution is a controlled evolution of joint state probability density subject to a co…
Set Invariance with Probability One for Controlled Diffusion: Score-based Approach
Wenqing Wang, Alexis M. H. Teter, Murat Arcak +1
Given a controlled diffusion and a connected, bounded, Lipschitz set, when is it possible to guarantee controlled set invariance with probability one? In this work, we answer this…
Markov Kernels, Distances and Optimal Control: A Parable of Linear Quadratic Non-Gaussian Distribution Steering
Alexis M. H. Teter, Wenqing Wang, Sachin Shivakumar +1
For a controllable linear time-varying (LTV) pair and positive semidefinite, we derive the Markov kernel for the Itô dif…
On the Hopf-Cole Transform for Control-affine Schrödinger Bridge
Alexis Teter, Abhishek Halder
The purpose of this note is to clarify the importance of the relation in solving control-affine Schrödinger bridge problem…
Schrödinger Bridge with Quadratic State Cost is Exactly Solvable
Alexis M. H. Teter, Wenqing Wang, Abhishek Halder
Schrödinger bridge is a diffusion process that steers a given distribution to another in a prescribed time while minimizing the effort to do so. It can be seen as the stochastic d…
Solution of the Probabilistic Lambert Problem: Connections with Optimal Mass Transport, Schrödinger Bridge and Reaction-Diffusion PDEs
Alexis M. H. Teter, Iman Nodozi, Abhishek Halder
The Lambert problem originated in orbital mechanics. It concerns with determining the initial velocity for a boundary value problem involving the dynamical constraint due to gravit…