# Finite Horizon Density Control for Static State Feedback Linearizable Systems

arXiv: https://arxiv.org/abs/1904.02272 · HTML: https://mlsanity.com/paper/1904.02272/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Apr 2019.

## Built on by (most cited first, 3 of 3)

- [A Physics-informed Deep Learning Approach for Minimum Effort Stochastic Control of Colloidal Self-Assembly](https://mlsanity.com/paper/2208.09182/) (2022)
- [Schr"odinger Bridge Over A Compact Connected Lie Group](https://mlsanity.com/paper/2603.14049/) (2026)
- [The Ground Cost for Optimal Transport of Angular Velocity](https://mlsanity.com/paper/2504.03190/) (2025)

## Abstract (arXiv)

We consider the problem of steering the joint state probability density function of a static feedback linearizable control system over finite time horizon. Potential applications include controlling neuronal populations, swarm guidance, and probabilistic motion planning. Our theoretical developments reveal the structure of the minimum energy controller for the same, and can be viewed as a generalization of the Benamou-Brenier theory for dynamic optimal transport. Further analytical results are derived for solving the feasibility problem, i.e., for finding feedback that steers a given joint density function to another in fixed time, subject to the controlled nonlinear dynamics. An algorithm based on the Schr"odinger bridge is proposed to approximate a feasible controller; a numerical example is worked out to illustrate the same.