High-Dimensional Optimal Density Control with Wasserstein Metric Matching
- Resource Type
- Conference
- Authors
- Ma, Shaojun; Hou, Mengxue; Ye, Xiaojing; Zhou, Haomin
- Source
- 2023 62nd IEEE Conference on Decision and Control (CDC) Decision and Control (CDC), 2023 62nd IEEE Conference on. :6813-6818 Dec, 2023
- Subject
- Computing and Processing
Power, Energy and Industry Applications
Robotics and Control Systems
Measurement
Costs
Computational modeling
Neural networks
Reduced order systems
Probability distribution
Numerical models
- Language
- ISSN
- 2576-2370
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 without collision 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.