# Exploiting Differential Flatness for Efficient Learning-based Model Predictive Control of Constrained Multi-Input Control Affine Systems

arXiv: https://arxiv.org/abs/2604.24706 · HTML: https://mlsanity.com/paper/2604.24706/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 20 references that are in the map.
- First posted on arXiv 27 Apr 2026.

## Builds on (most cited first, 9 of 9)

- [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)
- [acados: a modular open-source framework for fast embedded optimal control](https://mlsanity.com/paper/1910.13753/) (2019)
- [safe-control-gym: a Unified Benchmark Suite for Safe Learning-based Control and Reinforcement Learning in Robotics](https://mlsanity.com/paper/2109.06325/) (2021)
- [A Comparative Study of Nonlinear MPC and Differential-Flatness-Based Control for Quadrotor Agile Flight](https://mlsanity.com/paper/2109.01365/) (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)
- [Differentially Flat Learning-based Model Predictive Control Using a Stability, State, and Input Constraining Safety Filter](https://mlsanity.com/paper/2307.10541/) (2023)
- [A Computationally Efficient Learning-Based Model Predictive Control for Multirotors under Aerodynamic Disturbances](https://mlsanity.com/paper/2402.10323/) (2024)
- [Tiny Learning-Based MPC for Multirotors: Solver-Aware Learning for Efficient Embedded Predictive Control](https://mlsanity.com/paper/2410.23634/) (2024)

## Abstract (arXiv)

Learning-based control techniques use data from past trajectories to control systems with uncertain dynamics. However, learning-based controllers are often computationally inefficient, limiting their practicality. To address this limitation, we propose a learning-based controller that exploits differential flatness, a property of many robotic systems. Recent research on using flatness for learning-based control either is limited in that it (i) ignores input constraints, (ii) applies only to single-input systems, or (iii) is tailored to specific platforms. In contrast, our approach uses a system extension and block-diagonal cost formulation to control general multi-input, nonlinear, affine systems. Furthermore, it satisfies input and half-space flat state constraints and guarantees probabilistic Lyapunov decrease using only two sequential convex optimizations. We show that our approach performs similarly to, but is multiple times more efficient than, a Gaussian process model predictive controller in simulation, and achieves competitive tracking in real hardware experiments.