# A robust adaptive model predictive control framework for nonlinear uncertain systems

arXiv: https://arxiv.org/abs/1911.02899 · HTML: https://mlsanity.com/paper/1911.02899/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Nov 2019.

## Built on by (most cited first, 7 of 7)

- [Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learning](https://mlsanity.com/paper/2108.06266/) (2021)
- [Adaptive-Control-Oriented Meta-Learning for Nonlinear Systems](https://mlsanity.com/paper/2103.04490/) (2021)
- [Control-oriented meta-learning](https://mlsanity.com/paper/2204.06716/) (2022)
- [Bridging Model-based Safety and Model-free Reinforcement Learning through System Identification of Low Dimensional Linear Models](https://mlsanity.com/paper/2205.05787/) (2022)
- [A robust and adaptive MPC formulation for Gaussian process models](https://mlsanity.com/paper/2507.02098/) (2025)
- [A Framework for Adaptive Stabilisation of Nonlinear Stochastic Systems](https://mlsanity.com/paper/2511.17436/) (2025)
- [Consistent Model Chasing Is Minimax Optimal: The Exact Value of Scalar Adversarial Adaptive Control under Large Parametric Uncertainty](https://mlsanity.com/paper/2608.13651/) (2026)

## Abstract (arXiv)

In this paper, we present a tube-based framework for robust adaptive model predictive control (RAMPC) for nonlinear systems subject to parametric uncertainty and additive disturbances. Set-membership estimation is used to provide accurate bounds on the parametric uncertainty, which are employed for the construction of the tube in a robust MPC scheme. The resulting RAMPC framework ensures robust recursive feasibility and robust constraint satisfaction, while allowing for less conservative operation compared to robust MPC schemes without model/parameter adaptation. Furthermore, by using an additional mean-squared point estimate in the objective function the framework ensures finite-gain L2 stability w.r.t. additive disturbances. As a first contribution we derive suitable monotonicity and non-increasing properties on general parameter estimation algorithms and tube/set based RAMPC schemes that ensure robust recursive feasibility and robust constraint satisfaction under recursive model updates. Then, as the main contribution of this paper, we provide similar conditions for a tube based formulation that is parametrized using an incremental Lyapunov function, a scalar contraction rate and a function bounding the uncertainty. With this result, we can provide simple constructive designs for different RAMPC schemes with varying computational complexity and conservatism. As a corollary, we can demonstrate that state of the art formulations for nonlinear RAMPC are a special case of the proposed framework. We provide a numerical example that demonstrates the flexibility of the proposed framework and showcase improvements compared to state of the art approaches.