# Differentially Flat Learning-based Model Predictive Control Using a Stability, State, and Input Constraining Safety Filter

arXiv: https://arxiv.org/abs/2307.10541 · HTML: https://mlsanity.com/paper/2307.10541/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 19 references that are in the map.
- First posted on arXiv 20 Jul 2023.

## Builds on (most cited first, 4 of 4)

- [Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learning](https://mlsanity.com/paper/2108.06266/) (2021)
- [Cautious Model Predictive Control using Gaussian Process Regression](https://mlsanity.com/paper/1705.10702/) (2017)
- [Data-Driven MPC for Quadrotors](https://mlsanity.com/paper/2102.05773/) (2021)
- [Gaussian Process-based Min-norm Stabilizing Controller for Control-Affine Systems with Uncertain Input Effects and Dynamics](https://mlsanity.com/paper/2011.07183/) (2020)

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

- [Exploiting Differential Flatness for Efficient Learning-based Model Predictive Control of Constrained Multi-Input Control Affine Systems](https://mlsanity.com/paper/2604.24706/) (2026)

## Abstract (arXiv)

Learning-based optimal control algorithms control unknown systems using past trajectory data and a learned model of the system dynamics. These controllers use either a linear approximation of the learned dynamics, trading performance for faster computation, or nonlinear optimization methods, which typically perform better but can limit real-time applicability. In this work, we present a novel nonlinear controller that exploits differential flatness to achieve similar performance to state-of-the-art learning-based controllers but with significantly less computational effort. Differential flatness is a property of dynamical systems whereby nonlinear systems can be exactly linearized through a nonlinear input mapping. Here, the nonlinear transformation is learned as a Gaussian process and is used in a safety filter that guarantees, with high probability, stability as well as input and flat state constraint satisfaction. This safety filter is then used to refine inputs from a flat model predictive controller to perform constrained nonlinear learning-based optimal control through two successive convex optimizations. We compare our method to state-of-the-art learning-based control strategies and achieve similar performance, but with significantly better computational efficiency, while also respecting flat state and input constraints, and guaranteeing stability.