# Learning to Control an Unstable System with One Minute of Data: Leveraging Gaussian Process Differentiation in Predictive Control

arXiv: https://arxiv.org/abs/2103.04548 · HTML: https://mlsanity.com/paper/2103.04548/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 45 references that are in the map.
- First posted on arXiv 8 Mar 2021.

## Builds on (most cited first, 20 of 20)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [A Rewriting System for Convex Optimization Problems](https://mlsanity.com/paper/1709.04494/) (2017)
- [Kernel Interpolation for Scalable Structured Gaussian Processes (KISS-GP)](https://mlsanity.com/paper/1503.01057/) (2015)
- [Learning-based Model Predictive Control for Safe Exploration](https://mlsanity.com/paper/1803.08287/) (2018)
- [Gaussian Processes for Data-Efficient Learning in Robotics and Control](https://mlsanity.com/paper/1502.02860/) (2015)
- [Cautious Model Predictive Control using Gaussian Process Regression](https://mlsanity.com/paper/1705.10702/) (2017)
- [Neural Lander: Stable Drone Landing Control using Learned Dynamics](https://mlsanity.com/paper/1811.08027/) (2018)
- [Learning for Safety-Critical Control with Control Barrier Functions](https://mlsanity.com/paper/1912.10099/) (2019)
- [Safe Exploration for Interactive Machine Learning](https://mlsanity.com/paper/1910.13726/) (2019)
- [Safe Learning of Quadrotor Dynamics Using Barrier Certificates](https://mlsanity.com/paper/1710.05472/) (2017)
- [Robust Regression for Safe Exploration in Control](https://mlsanity.com/paper/1906.05819/) (2019)
- [Robust Guarantees for Perception-Based Control](https://mlsanity.com/paper/1907.03680/) (2019)
- [Neural-Swarm: Decentralized Close-Proximity Multirotor Control Using Learned Interactions](https://mlsanity.com/paper/2003.02992/) (2020)
- [Episodic Learning with Control Lyapunov Functions for Uncertain Robotic Systems](https://mlsanity.com/paper/1903.01577/) (2019)
- [Adaptive MPC for Iterative Tasks](https://mlsanity.com/paper/1804.09831/) (2018)
- [Chance-Constrained Trajectory Optimization for Safe Exploration and Learning of Nonlinear Systems](https://mlsanity.com/paper/2005.04374/) (2020)
- [Learning How to Autonomously Race a Car: a Predictive Control Approach](https://mlsanity.com/paper/1901.08184/) (2019)
- [GP-ILQG: Data-driven Robust Optimal Control for Uncertain Nonlinear Dynamical Systems](https://mlsanity.com/paper/1705.05344/) (2017)
- [Bayesian model predictive control: Efficient model exploration and regret bounds using posterior sampling](https://mlsanity.com/paper/2005.11744/) (2020)
- [Control of Unknown Nonlinear Systems with Linear Time-Varying MPC](https://mlsanity.com/paper/2004.03041/) (2020)

## Abstract (arXiv)

We present a straightforward and efficient way to control unstable robotic systems using an estimated dynamics model. Specifically, we show how to exploit the differentiability of Gaussian Processes to create a state-dependent linearized approximation of the true continuous dynamics that can be integrated with model predictive control. Our approach is compatible with most Gaussian process approaches for system identification, and can learn an accurate model using modest amounts of training data. We validate our approach by learning the dynamics of an unstable system such as a segway with a 7-D state space and 2-D input space (using only one minute of data), and we show that the resulting controller is robust to unmodelled dynamics and disturbances, while state-of-the-art control methods based on nominal models can fail under small perturbations. Code is open sourced at https://github.com/learning-and-control/core .