# Adaptive Robust Model Predictive Control via Uncertainty Cancellation

arXiv: https://arxiv.org/abs/2212.01371 · HTML: https://mlsanity.com/paper/2212.01371/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 52 references that are in the map.
- First posted on arXiv 2 Dec 2022.

## Builds on (most cited first, 19 of 19)

- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [A Tour of Reinforcement Learning: The View from Continuous Control](https://mlsanity.com/paper/1806.09460/) (2018)
- [Learning-based Model Predictive Control for Safe Exploration](https://mlsanity.com/paper/1803.08287/) (2018)
- [Cautious Model Predictive Control using Gaussian Process Regression](https://mlsanity.com/paper/1705.10702/) (2017)
- [Regret Bounds for Robust Adaptive Control of the Linear Quadratic Regulator](https://mlsanity.com/paper/1805.09388/) (2018)
- [Active Learning for Nonlinear System Identification with Guarantees](https://mlsanity.com/paper/2006.10277/) (2020)
- [Meta-Learning Priors for Efficient Online Bayesian Regression](https://mlsanity.com/paper/1807.08912/) (2018)
- [Adaptive-Control-Oriented Meta-Learning for Nonlinear Systems](https://mlsanity.com/paper/2103.04490/) (2021)
- [Safely Learning to Control the Constrained Linear Quadratic Regulator](https://mlsanity.com/paper/1809.10121/) (2018)
- [Regret Bounds for Adaptive Nonlinear Control](https://mlsanity.com/paper/2011.13101/) (2020)
- [Bayesian Learning-Based Adaptive Control for Safety Critical Systems](https://mlsanity.com/paper/1910.02325/) (2019)
- [Adaptive MPC for Iterative Tasks](https://mlsanity.com/paper/1804.09831/) (2018)
- [Asynchronous Deep Model Reference Adaptive Control](https://mlsanity.com/paper/2011.02920/) (2020)
- [Linear robust adaptive model predictive control: Computational complexity and conservatism -- extended version](https://mlsanity.com/paper/1909.01813/) (2019)
- [Meta-Learning-Based Robust Adaptive Flight Control Under Uncertain Wind Conditions](https://mlsanity.com/paper/2103.01932/) (2021)
- [Adaptive Robust Model Predictive Control with Matched and Unmatched Uncertainty](https://mlsanity.com/paper/2104.08261/) (2021)
- [Indirect-adaptive Model Predictive Control for Linear Systems with Polytopic Uncertainty](https://mlsanity.com/paper/1509.07170/) (2015)
- [A Semi-Definite Programming Approach to Robust Adaptive MPC under State Dependent Uncertainty](https://mlsanity.com/paper/1910.04378/) (2019)

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

- [Information-Theoretic Framework for Self-Adapting Model Predictive Controllers](https://mlsanity.com/paper/2603.01286/) (2026)

## Abstract (arXiv)

We propose a learning-based robust predictive control algorithm that compensates for significant uncertainty in the dynamics for a class of discrete-time systems that are nominally linear with an additive nonlinear component. Such systems commonly model the nonlinear effects of an unknown environment on a nominal system. We optimize over a class of nonlinear feedback policies inspired by certainty equivalent "estimate-and-cancel" control laws pioneered in classical adaptive control to achieve significant performance improvements in the presence of uncertainties of large magnitude, a setting in which existing learning-based predictive control algorithms often struggle to guarantee safety. In contrast to previous work in robust adaptive MPC, our approach allows us to take advantage of structure (i.e., the numerical predictions) in the a priori unknown dynamics learned online through function approximation. Our approach also extends typical nonlinear adaptive control methods to systems with state and input constraints even when we cannot directly cancel the additive uncertain function from the dynamics. We apply contemporary statistical estimation techniques to certify the system's safety through persistent constraint satisfaction with high probability. Moreover, we propose using Bayesian meta-learning algorithms that learn calibrated model priors to help satisfy the assumptions of the control design in challenging settings. Finally, we show in simulation that our method can accommodate more significant unknown dynamics terms than existing methods and that the use of Bayesian meta-learning allows us to adapt to the test environments more rapidly.