# Immersion-based model predictive control of constrained nonlinear systems: Polyflow approximation

arXiv: https://arxiv.org/abs/2011.13255 · HTML: https://mlsanity.com/paper/2011.13255/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Nov 2020.

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

- [Learning Noise-Robust Stable Koopman Operator for Control with Hankel DMD](https://mlsanity.com/paper/2408.06607/) (2024)

## Abstract (arXiv)

In the framework of Model Predictive Control (MPC), the control input is typically computed by solving optimization problems repeatedly online. For general nonlinear systems, the online optimization problems are non-convex and computationally expensive or even intractable. In this paper, we propose to circumvent this issue by computing a high-dimensional linear embedding of discrete-time nonlinear systems. The computation relies on an algebraic condition related to the immersibility property of nonlinear systems and can be implemented offline. With the high-dimensional linear model, we then define and solve a convex online MPC problem. We also provide an interpretation of our approach under the Koopman operator framework.