# Finite Horizon Density Steering for Multi-input State Feedback Linearizable Systems

arXiv: https://arxiv.org/abs/1909.12511 · HTML: https://mlsanity.com/paper/1909.12511/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Sep 2019.

## Built on by (most cited first, 11 of 11)

- [Neural Schr"odinger Bridge with Sinkhorn Losses: Application to Data-driven Minimum Effort Control of Colloidal Self-assembly](https://mlsanity.com/paper/2307.14442/) (2023)
- [A Physics-informed Deep Learning Approach for Minimum Effort Stochastic Control of Colloidal Self-Assembly](https://mlsanity.com/paper/2208.09182/) (2022)
- [On the Hopf-Cole Transform for Control-affine Schr"odinger Bridge](https://mlsanity.com/paper/2503.17640/) (2025)
- [Stochastic Learning of Computational Resource Usage as Graph Structured Multimarginal Schr"odinger Bridge](https://mlsanity.com/paper/2405.12463/) (2024)
- [A Generalized Sinkhorn Algorithm for Mean-Field Schr"odinger Bridge](https://mlsanity.com/paper/2604.06531/) (2026)
- [Score Matching Diffusion Based Feedback Control and Planning of Nonlinear Systems](https://mlsanity.com/paper/2504.09836/) (2025)
- [Schr"odinger Bridge Over A Compact Connected Lie Group](https://mlsanity.com/paper/2603.14049/) (2026)
- [Optimal Mass Transport over the Euler Equation](https://mlsanity.com/paper/2304.00595/) (2023)
- [Nonlinear Non-Gaussian Density Steering with Input and Noise Channel Mismatch: Sinkhorn with Memory for Solving the Control-affine Schr"odinger Bridge Problem](https://mlsanity.com/paper/2604.23370/) (2026)
- [The Ground Cost for Optimal Transport of Angular Velocity](https://mlsanity.com/paper/2504.03190/) (2025)
- [On the Equivalence of Stochastic Control and Path Space Formulations for Schr"odinger Bridges over Compact Connected Lie Groups](https://mlsanity.com/paper/2609.13758/) (2026)

## Abstract (arXiv)

In this paper, we study the feedback synthesis problem for steering the joint state density or ensemble subject to multi-input state feedback linearizable dynamics. This problem is of interest to many practical applications including that of dynamically shaping a robotic swarm. Our results here show that it is possible to exploit the structural nonlinearities to derive the feedback controllers steering the joint density from a prescribed shape to another while minimizing the expected control effort to do so. The developments herein build on our previous work, and extend the theory of the Schr"odinger bridge problem subject to feedback linearizable dynamics.