# Learning Model Predictive Control for iterative tasks. A Data-Driven Control Framework

arXiv: https://arxiv.org/abs/1609.01387 · HTML: https://mlsanity.com/paper/1609.01387/

## Key facts

- Cited by 39 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Sep 2016.

## Built on by (most cited first, 30 of 39)

- [Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learning](https://mlsanity.com/paper/2108.06266/) (2021)
- [A Review of Safe Reinforcement Learning: Methods, Theory and Applications](https://mlsanity.com/paper/2205.10330/) (2022)
- [The Safety Filter: A Unified View of Safety-Critical Control in Autonomous Systems](https://mlsanity.com/paper/2309.05837/) (2023)
- [LyaNet: A Lyapunov Framework for Training Neural ODEs](https://mlsanity.com/paper/2202.02526/) (2022)
- [Lessons from AlphaZero for Optimal, Model Predictive, and Adaptive Control](https://mlsanity.com/paper/2108.10315/) (2021)
- [Neural Operators of Backstepping Controller and Observer Gain Functions for Reaction-Diffusion PDEs](https://mlsanity.com/paper/2303.10506/) (2023)
- [Scalable Learning of Safety Guarantees for Autonomous Systems using Hamilton-Jacobi Reachability](https://mlsanity.com/paper/2101.05916/) (2021)
- [Robust Uncertainty Bounds in Reproducing Kernel Hilbert Spaces: A Convex Optimization Approach](https://mlsanity.com/paper/2104.09582/) (2021)
- [Learning to Optimize in Model Predictive Control](https://mlsanity.com/paper/2212.02603/) (2022)
- [LS3: Latent Space Safe Sets for Long-Horizon Visuomotor Control of Sparse Reward Iterative Tasks](https://mlsanity.com/paper/2107.04775/) (2021)
- [Learning Sampling Distributions for Model Predictive Control](https://mlsanity.com/paper/2212.02587/) (2022)
- [A Regret Minimization Approach to Iterative Learning Control](https://mlsanity.com/paper/2102.13478/) (2021)
- [Deep Model Predictive Optimization](https://mlsanity.com/paper/2310.04590/) (2023)
- [Model Predictive Control and Reinforcement Learning: A Unified Framework Based on Dynamic Programming](https://mlsanity.com/paper/2406.00592/) (2024)
- [SAFER: Data-Efficient and Safe Reinforcement Learning via Skill Acquisition](https://mlsanity.com/paper/2202.04849/) (2022)
- [Equipping Black-Box Policies with Model-Based Advice for Stable Nonlinear Control](https://mlsanity.com/paper/2206.01341/) (2022)
- [Safe Reinforcement Learning via Confidence-Based Filters](https://mlsanity.com/paper/2207.01337/) (2022)
- [Model Predictive Control via On-Policy Imitation Learning](https://mlsanity.com/paper/2210.09206/) (2022)
- [Safe Reach Set Computation via Neural Barrier Certificates](https://mlsanity.com/paper/2404.18813/) (2024)
- [Automated Controller Calibration by Kalman Filtering](https://mlsanity.com/paper/2111.10832/) (2021)
- [MPC-Inspired Reinforcement Learning for Verifiable Model-Free Control](https://mlsanity.com/paper/2312.05332/) (2023)
- [Revisiting Tropical Polynomial Division: Theory, Algorithms and Application to Neural Networks](https://mlsanity.com/paper/2306.15157/) (2023)
- [DeepSafeMPC: Deep Learning-Based Model Predictive Control for Safe Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2403.06397/) (2024)
- [Safe Deep Model-Based Reinforcement Learning with Lyapunov Functions](https://mlsanity.com/paper/2405.16184/) (2024)
- [A Simple Approach to Constraint-Aware Imitation Learning with Application to Autonomous Racing](https://mlsanity.com/paper/2503.07737/) (2025)
- [SOCKS: A Stochastic Optimal Control and Reachability Toolbox Using Kernel Methods](https://mlsanity.com/paper/2203.06290/) (2022)
- [Out-of-Distribution-Aware Electric Vehicle Charging](https://mlsanity.com/paper/2311.05941/) (2023)
- [Reinforcement Learning Compensated Model Predictive Control for Off-road Driving on Unknown Deformable Terrain](https://mlsanity.com/paper/2408.09253/) (2024)
- [A New Perspective On AI Safety Through Control Theory Methodologies](https://mlsanity.com/paper/2506.23703/) (2025)
- [Uncertainty-Aware Predictive Safety Filters for Probabilistic Neural Network Dynamics](https://mlsanity.com/paper/2604.26836/) (2026)

## Abstract (arXiv)

A Learning Model Predictive Controller (LMPC) for iterative tasks is presented. The controller is reference-free and is able to improve its performance by learning from previous iterations. A safe set and a terminal cost function are used in order to guarantee recursive feasibility and non-increasing performance at each iteration. The paper presents the control design approach, and shows how to recursively construct terminal set and terminal cost from state and input trajectories of previous iterations. Simulation results show the effectiveness of the proposed control logic.