High-dimensional Optimal Density Control with Wasserstein Metric Matching


We present a novel computational framework for density control in high-dimensional state spaces. The considered dynamical system consists of a large number of indistinguishable agents whose behaviors can be collectively modeled as a time-evolving probability distribution. The goal is to steer the agents from an initial distribution to reach (or approximate) a given target distribution within a fixed time horizon at minimum cost. To tackle this problem, we propose to model the drift as a nonlinear reduced-order model, such as a deep network, and enforce the matching to the target distribution at terminal time either strictly or approximately using the Wasserstein metric. The resulting saddle-point problem can be solved by an effective numerical algorithm that leverages the excellent representation power of deep networks and fast automatic differentiation for this challenging high-dimensional control problem. A variety of numerical experiments were conducted to demonstrate the performance of our method.

In 2023 Conference on Decision and Control
Mengxue Hou
Mengxue Hou
Assistant Professor, Electrical Engineering

My research interests include robotic autonomy, mobile sensor networks, and human robot interaction. I aim to devise practical, computationally-efficient, and provably-correct algorithms that prepare robotic systems to be cognizant, taskable, and adaptive, and can collaborate with human operators to co-exist in a complex, ever-changing and unknown environment.