# ABC-LMPC: Safe Sample-Based Learning MPC for Stochastic Nonlinear Dynamical Systems with Adjustable Boundary Conditions

arXiv: https://arxiv.org/abs/2003.01410 · HTML: https://mlsanity.com/paper/2003.01410/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Mar 2020.

## Built on by (most cited first, 8 of 8)

- [Optimal Cost Design for Model Predictive Control](https://mlsanity.com/paper/2104.11353/) (2021)
- [Policy Gradient Bayesian Robust Optimization for Imitation Learning](https://mlsanity.com/paper/2106.06499/) (2021)
- [LS3: Latent Space Safe Sets for Long-Horizon Visuomotor Control of Sparse Reward Iterative Tasks](https://mlsanity.com/paper/2107.04775/) (2021)
- [MESA: Offline Meta-RL for Safe Adaptation and Fault Tolerance](https://mlsanity.com/paper/2112.03575/) (2021)
- [Safe Model-based Off-policy Reinforcement Learning for Eco-Driving in Connected and Automated Hybrid Electric Vehicles](https://mlsanity.com/paper/2105.11640/) (2021)
- [SAFER: Data-Efficient and Safe Reinforcement Learning via Skill Acquisition](https://mlsanity.com/paper/2202.04849/) (2022)
- [Safe Deep Model-Based Reinforcement Learning with Lyapunov Functions](https://mlsanity.com/paper/2405.16184/) (2024)
- [SIT-LMPC: Safe Information-Theoretic Learning Model Predictive Control for Iterative Tasks](https://mlsanity.com/paper/2602.16187/) (2026)

## Abstract (arXiv)

Sample-based learning model predictive control (LMPC) strategies have recently attracted attention due to their desirable theoretical properties and their good empirical performance on robotic tasks. However, prior analysis of LMPC controllers for stochastic systems has mainly focused on linear systems in the iterative learning control setting. We present a novel LMPC algorithm, Adjustable Boundary Condition LMPC (ABC-LMPC), which enables rapid adaptation to novel start and goal configurations and theoretically show that the resulting controller guarantees iterative improvement in expectation for stochastic nonlinear systems. We present results with a practical instantiation of this algorithm and experimentally demonstrate that the resulting controller adapts to a variety of initial and terminal conditions on 3 stochastic continuous control tasks.