9 papers · 1 filter
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 con…
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 diff…
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 problems v…
Weyl Calculus and Exactly Solvable Schrödinger Bridges with Quadratic State Cost
Alexis M. H. Teter, Wenqing Wang, Abhishek Halder
Schrödinger bridge--a stochastic dynamical generalization of optimal mass transport--exhibits a learning-control duality. Viewed as a stochastic control problem, the Schrödinger br…
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 dy…
Solution of the Probabilistic Lambert's Problem: Optimal Transport Approach
Alexis M. H. Teter, Iman Nodozi, Abhishek Halder
The deterministic variant of the Lambert's problem was posed by Lambert in the 18th century and its solution for conic trajectory has been derived by many, including Euler, Lambert…
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…
On the Contraction Coefficient of the Schrödinger Bridge for Stochastic Linear Systems
Alexis M. H. Teter, Yongxin Chen, Abhishek Halder
Schrödinger bridge is a stochastic optimal control problem to steer a given initial state density to another, subject to controlled diffusion and deadline constraints. A popular me…