# Sampling-Based Robust Control of Autonomous Systems with Non-Gaussian Noise

arXiv: https://arxiv.org/abs/2110.12662 · HTML: https://mlsanity.com/paper/2110.12662/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 58 references that are in the map.
- First posted on arXiv 25 Oct 2021.

## Builds on (most cited first, 22 of 22)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learning](https://mlsanity.com/paper/2108.06266/) (2021)
- [Safe Model-based Reinforcement Learning with Stability Guarantees](https://mlsanity.com/paper/1705.08551/) (2017)
- [Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations](https://mlsanity.com/paper/1505.05116/) (2015)
- [Hamilton-Jacobi Reachability: A Brief Overview and Recent Advances](https://mlsanity.com/paper/1709.07523/) (2017)
- [A General Safety Framework for Learning-Based Control in Uncertain Robotic Systems](https://mlsanity.com/paper/1705.01292/) (2017)
- [Learning-based Model Predictive Control for Safe Exploration](https://mlsanity.com/paper/1803.08287/) (2018)
- [Cautious Model Predictive Control using Gaussian Process Regression](https://mlsanity.com/paper/1705.10702/) (2017)
- [Learning for Safety-Critical Control with Control Barrier Functions](https://mlsanity.com/paper/1912.10099/) (2019)
- [Probably Approximately Correct MDP Learning and Control With Temporal Logic Constraints](https://mlsanity.com/paper/1404.7073/) (2014)
- [PAC Statistical Model Checking for Markov Decision Processes and Stochastic Games](https://mlsanity.com/paper/1905.04403/) (2019)
- [FaSTrack: a Modular Framework for Fast and Guaranteed Safe Motion Planning](https://mlsanity.com/paper/1703.07373/) (2017)
- [Automated Verification and Synthesis of Stochastic Hybrid Systems: A Survey](https://mlsanity.com/paper/2101.07491/) (2021)
- [Deep Reinforcement Learning Attitude Control of Fixed-Wing UAVs Using Proximal Policy Optimization](https://mlsanity.com/paper/1911.05478/) (2019)
- [StocHy: automated verification and synthesis of stochastic processes](https://mlsanity.com/paper/1901.10287/) (2019)
- [Unified Multi-Rate Control: from Low Level Actuation to High Level Planning](https://mlsanity.com/paper/2012.06558/) (2020)
- [ProbReach: Verified Probabilistic Delta-Reachability for Stochastic Hybrid Systems](https://mlsanity.com/paper/1410.8060/) (2014)
- [Scenario-Based Verification of Uncertain MDPs](https://mlsanity.com/paper/1912.11223/) (2019)
- [Correct-by-construction reach-avoid control of partially observable linear stochastic systems](https://mlsanity.com/paper/2103.02398/) (2021)
- [Multi-objective Robust Strategy Synthesis for Interval Markov Decision Processes](https://mlsanity.com/paper/1706.06875/) (2017)
- [Voronoi Partition-based Scenario Reduction for Fast Sampling-based Stochastic Reachability Computation of LTI Systems](https://mlsanity.com/paper/1811.03643/) (2018)
- [Benchmarks for cyber-physical systems: A modular model library for building automation systems (Extended version)](https://mlsanity.com/paper/1803.06315/) (2018)

## Built on by (most cited first, 13 of 13)

- [Robust Control for Dynamical Systems With Non-Gaussian Noise via Formal Abstractions](https://mlsanity.com/paper/2301.01526/) (2023)
- [Compositional Policy Learning in Stochastic Control Systems with Formal Guarantees](https://mlsanity.com/paper/2312.01456/) (2023)
- [Probabilities Are Not Enough: Formal Controller Synthesis for Stochastic Dynamical Models with Epistemic Uncertainty](https://mlsanity.com/paper/2210.05989/) (2022)
- [Decision-Making Under Uncertainty: Beyond Probabilities](https://mlsanity.com/paper/2303.05848/) (2023)
- [Formal Verification of Unknown Dynamical Systems via Gaussian Process Regression](https://mlsanity.com/paper/2201.00655/) (2021)
- [An Analysis of Model-Based Reinforcement Learning From Abstracted Observations](https://mlsanity.com/paper/2208.14407/) (2022)
- [Certified Policy Verification and Synthesis for MDPs under Distributional Reach-avoidance Properties](https://mlsanity.com/paper/2405.04015/) (2024)
- [Data-driven Abstractions with Probabilistic Guarantees for Linear PETC Systems](https://mlsanity.com/paper/2203.05522/) (2022)
- [Formal Controller Synthesis for Markov Jump Linear Systems with Uncertain Dynamics](https://mlsanity.com/paper/2212.00679/) (2022)
- [Robust Parameter Learning for Uncertain MDPs](https://mlsanity.com/paper/2605.01339/) (2026)
- [Correct-by-Construction Control for Stochastic and Uncertain Dynamical Models via Formal Abstractions](https://mlsanity.com/paper/2311.09786/) (2023)
- [Efficient Distribution Learning with Error Bounds in Wasserstein Distance](https://mlsanity.com/paper/2602.08063/) (2026)
- [Safety Certification is Classification](https://mlsanity.com/paper/2605.06087/) (2026)

## Abstract (arXiv)

Controllers for autonomous systems that operate in safety-critical settings must account for stochastic disturbances. Such disturbances are often modelled as process noise, and common assumptions are that the underlying distributions are known and/or Gaussian. In practice, however, these assumptions may be unrealistic and can lead to poor approximations of the true noise distribution. We present a novel planning method that does not rely on any explicit representation of the noise distributions. In particular, we address the problem of computing a controller that provides probabilistic guarantees on safely reaching a target. First, we abstract the continuous system into a discrete-state model that captures noise by probabilistic transitions between states. As a key contribution, we adapt tools from the scenario approach to compute probably approximately correct (PAC) bounds on these transition probabilities, based on a finite number of samples of the noise. We capture these bounds in the transition probability intervals of a so-called interval Markov decision process (iMDP). This iMDP is robust against uncertainty in the transition probabilities, and the tightness of the probability intervals can be controlled through the number of samples. We use state-of-the-art verification techniques to provide guarantees on the iMDP, and compute a controller for which these guarantees carry over to the autonomous system. Realistic benchmarks show the practical applicability of our method, even when the iMDP has millions of states or transitions.