# Model Predictive Tracking Control for Invariant Systems on Matrix Lie Groups via Stable Embedding into Euclidean Spaces

arXiv: https://arxiv.org/abs/1910.05669 · HTML: https://mlsanity.com/paper/1910.05669/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Oct 2019.

## Built on by (most cited first, 1 of 1)

- [Feedback Gradient Descent: Efficient and Stable Optimization with Orthogonality for DNNs](https://mlsanity.com/paper/2205.08385/) (2022)

## Abstract (arXiv)

For controller design for systems on manifolds embedded in Euclidean space, it is convenient to utilize a theory that requires a single global coordinate system on the ambient Euclidean space rather than multiple local charts on the manifold or coordinate-free tools from differential geometry. In this article, we apply such a theory to design model predictive tracking controllers for systems whose dynamics evolve on manifolds and illustrate its efficacy with the fully actuated rigid body attitude control system.