A computationally efficient robust model predictive control framework for uncertain nonlinear systems -- extended version
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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).
Key facts. Cited by 14 papers in the map (data through 14 Oct 2026). First posted on arXiv 26 Oct 2019.
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Citing papers per year: 2021: 1; 2022: 1; 2023: 4; 2024: 3; 2025: 1; 2026: 4.
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- 2024Safety Filtering While Training: Improving the Performance and Sample Efficiency of Reinforcement Learning Agentscited by 17
- 2023Automatic nonlinear MPC approximation with closed-loop guaranteescited by 12
- 2023Approximate non-linear model predictive control with safety-augmented neural networkscited by 9
- 2024Parameter-Adaptive Approximate MPC: Tuning Neural-Network Controllers without Retrainingcited by 7
- 2026Safe Large-Scale Robust Nonlinear MPC in Milliseconds via Reachability-Constrained System Level Synthesis on the GPUcited by 7
- 2023Multi-Step Model Predictive Safety Filters: Reducing Chattering by Increasing the Prediction Horizoncited by 5
- 2023Learning Predictive Safety Filter via Decomposition of Robust Invariant Setcited by 3
- 2024LiRA: Light-Robust Adversary for Model-based Reinforcement Learning in Real Worldcited by 3
- 2021Combining Gaussian processes and polynomial chaos expansions for stochastic nonlinear model predictive controlcited by 1
- 2026Uncertainty-Aware Predictive Safety Filters for Probabilistic Neural Network Dynamicscited by 1
- 2022A stabilizing reinforcement learning approach for sampled systems with partially unknown modelscited by 0
- 2025A robust and adaptive MPC formulation for Gaussian process modelscited by 0
- 2026RL-Guided PAC-NMPC for Probabilistically-Safe Perception-Based Navigation in Unknown Environments30 Sep 2026
- 2026Topological Feasibility Guarantees for Differentiable Predictive Control11 Aug 2026
- 2026Uncertainty-Aware Predictive Safety Filters for Probabilistic Neural Network Dynamics29 Apr 2026
- 2026Safe Large-Scale Robust Nonlinear MPC in Milliseconds via Reachability-Constrained System Level Synthesis on the GPU8 Apr 2026
- 2025A robust and adaptive MPC formulation for Gaussian process models2 Jul 2025
- 2024Safety Filtering While Training: Improving the Performance and Sample Efficiency of Reinforcement Learning Agents15 Oct 2024
- 2024LiRA: Light-Robust Adversary for Model-based Reinforcement Learning in Real World29 Sep 2024
- 2024Parameter-Adaptive Approximate MPC: Tuning Neural-Network Controllers without Retraining8 Apr 2024
- 2023Automatic nonlinear MPC approximation with closed-loop guarantees15 Dec 2023
- 2023Learning Predictive Safety Filter via Decomposition of Robust Invariant Set12 Nov 2023
- 2023Multi-Step Model Predictive Safety Filters: Reducing Chattering by Increasing the Prediction Horizon20 Sep 2023
- 2023Approximate non-linear model predictive control with safety-augmented neural networks19 Apr 2023
- 2024Safety Filtering While Training: Improving the Performance and Sample Efficiency of Reinforcement Learning Agentscited by 17
- 2024LiRA: Light-Robust Adversary for Model-based Reinforcement Learning in Real Worldcited by 3
- 2026Uncertainty-Aware Predictive Safety Filters for Probabilistic Neural Network Dynamicscited by 1
- 2026RL-Guided PAC-NMPC for Probabilistically-Safe Perception-Based Navigation in Unknown Environmentscited by 0
- 2026RL-Guided PAC-NMPC for Probabilistically-Safe Perception-Based Navigation in Unknown Environments30 Sep 2026
- 2026Uncertainty-Aware Predictive Safety Filters for Probabilistic Neural Network Dynamics29 Apr 2026
- 2024Safety Filtering While Training: Improving the Performance and Sample Efficiency of Reinforcement Learning Agents15 Oct 2024
- 2024LiRA: Light-Robust Adversary for Model-based Reinforcement Learning in Real World29 Sep 2024
- 2023Automatic nonlinear MPC approximation with closed-loop guaranteescited by 12
- 2023Approximate non-linear model predictive control with safety-augmented neural networkscited by 9
- 2024Parameter-Adaptive Approximate MPC: Tuning Neural-Network Controllers without Retrainingcited by 7
- 2026Safe Large-Scale Robust Nonlinear MPC in Milliseconds via Reachability-Constrained System Level Synthesis on the GPUcited by 7
- 2023Multi-Step Model Predictive Safety Filters: Reducing Chattering by Increasing the Prediction Horizoncited by 5
- 2023Learning Predictive Safety Filter via Decomposition of Robust Invariant Setcited by 3
- 2021Combining Gaussian processes and polynomial chaos expansions for stochastic nonlinear model predictive controlcited by 1
- 2022A stabilizing reinforcement learning approach for sampled systems with partially unknown modelscited by 0
- 2025A robust and adaptive MPC formulation for Gaussian process modelscited by 0
- 2026Topological Feasibility Guarantees for Differentiable Predictive Controlcited by 0
- 2026Topological Feasibility Guarantees for Differentiable Predictive Control11 Aug 2026
- 2026Safe Large-Scale Robust Nonlinear MPC in Milliseconds via Reachability-Constrained System Level Synthesis on the GPU8 Apr 2026
- 2025A robust and adaptive MPC formulation for Gaussian process models2 Jul 2025
- 2024Parameter-Adaptive Approximate MPC: Tuning Neural-Network Controllers without Retraining8 Apr 2024
- 2023Automatic nonlinear MPC approximation with closed-loop guarantees15 Dec 2023
- 2023Learning Predictive Safety Filter via Decomposition of Robust Invariant Set12 Nov 2023
- 2023Multi-Step Model Predictive Safety Filters: Reducing Chattering by Increasing the Prediction Horizon20 Sep 2023
- 2023Approximate non-linear model predictive control with safety-augmented neural networks19 Apr 2023
- 2022A stabilizing reinforcement learning approach for sampled systems with partially unknown models31 Aug 2022
- 2021Combining Gaussian processes and polynomial chaos expansions for stochastic nonlinear model predictive control9 Mar 2021