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Speaker: Abhishek Halder, Iowa State University
Title: Probabilistic Lambert Problem: Connections with Optimal Mass Transport, Schrödinger Bridge, and Reaction-Diffusion PDEs
Abstract: The Lambert problem originated in the 18th century and in its original form, is a problem in classical mechanics. Its solution has application in steering a spacecraft from a given initial to a given terminal position within prescribed flight time via velocity control. In this talk, I will consider the probabilistic Lambert problem that has received significant attention in astrodynamics community in the 21st century. I will explain that the probabilistic Lambert problem is a variant of the optimal mass transport problem, the latter topic being a workhorse in modern machine learning and stochastic control. Establishing this connection between the two problems of contemporary interest helps us to prove theoretical properties of the solution. The same connection also helps in designing novel numerical algorithm to solve this problem using entropy-regularized optimal transport known as the Schrödinger bridge. We show that our analyses lead to solving a system of reaction-diffusion PDEs where the gravitational potential appears as the reaction rate.