# A computationally efficient robust model predictive control framework for uncertain nonlinear systems -- extended version

arXiv: https://arxiv.org/abs/1910.12081 · HTML: https://mlsanity.com/paper/1910.12081/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Oct 2019.

## Built on by (most cited first, 14 of 14)

- [Safety Filtering While Training: Improving the Performance and Sample Efficiency of Reinforcement Learning Agents](https://mlsanity.com/paper/2410.11671/) (2024)
- [Automatic nonlinear MPC approximation with closed-loop guarantees](https://mlsanity.com/paper/2312.10199/) (2023)
- [Approximate non-linear model predictive control with safety-augmented neural networks](https://mlsanity.com/paper/2304.09575/) (2023)
- [Parameter-Adaptive Approximate MPC: Tuning Neural-Network Controllers without Retraining](https://mlsanity.com/paper/2404.05835/) (2024)
- [Safe Large-Scale Robust Nonlinear MPC in Milliseconds via Reachability-Constrained System Level Synthesis on the GPU](https://mlsanity.com/paper/2604.07644/) (2026)
- [Multi-Step Model Predictive Safety Filters: Reducing Chattering by Increasing the Prediction Horizon](https://mlsanity.com/paper/2309.11453/) (2023)
- [Learning Predictive Safety Filter via Decomposition of Robust Invariant Set](https://mlsanity.com/paper/2311.06769/) (2023)
- [LiRA: Light-Robust Adversary for Model-based Reinforcement Learning in Real World](https://mlsanity.com/paper/2409.19617/) (2024)
- [Combining Gaussian processes and polynomial chaos expansions for stochastic nonlinear model predictive control](https://mlsanity.com/paper/2103.05441/) (2021)
- [Uncertainty-Aware Predictive Safety Filters for Probabilistic Neural Network Dynamics](https://mlsanity.com/paper/2604.26836/) (2026)
- [A stabilizing reinforcement learning approach for sampled systems with partially unknown models](https://mlsanity.com/paper/2208.14714/) (2022)
- [A robust and adaptive MPC formulation for Gaussian process models](https://mlsanity.com/paper/2507.02098/) (2025)
- [Topological Feasibility Guarantees for Differentiable Predictive Control](https://mlsanity.com/paper/2608.10332/) (2026)
- [RL-Guided PAC-NMPC for Probabilistically-Safe Perception-Based Navigation in Unknown Environments](https://mlsanity.com/paper/2609.39854/) (2026)

## Abstract (arXiv)

In this paper, we present a nonlinear robust model predictive control (MPC) framework for general (state and input dependent) disturbances. This approach uses an online constructed tube in order to tighten the nominal (state and input) constraints. To facilitate an efficient online implementation, the shape of the tube is based on an offline computed incremental Lyapunov function with a corresponding (nonlinear) incrementally stabilizing feedback. Crucially, the online optimization only implicitly includes these nonlinear functions in terms of scalar bounds, which enables an efficient implementation. Furthermore, to account for an efficient evaluation of the worst case disturbance, a simple function is constructed offline that upper bounds the possible disturbance realizations in a neighbourhood of a given point of the open-loop trajectory. The resulting MPC scheme ensures robust constraint satisfaction and practical asymptotic stability with a moderate increase in the online computational demand compared to a nominal MPC. We demonstrate the applicability of the proposed framework in comparison to state of the art robust MPC approaches with a nonlinear benchmark example. This paper is an extended version of [1], and contains further details and additional considers: continuous-time systems (App. A), more general nonlinear constraints (App. B) and special cases (Sec. IV).