# Robust Control for Dynamical Systems With Non-Gaussian Noise via Formal Abstractions

arXiv: https://arxiv.org/abs/2301.01526 · HTML: https://mlsanity.com/paper/2301.01526/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 94 references that are in the map.
- First posted on arXiv 4 Jan 2023.

## Builds on (most cited first, 30 of 33)

- [Sim-to-Real Transfer of Robotic Control with Dynamics Randomization](https://mlsanity.com/paper/1710.06537/) (2017)
- [Robust Adversarial Reinforcement Learning](https://mlsanity.com/paper/1703.02702/) (2017)
- [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)
- [Robust Reinforcement Learning using Adversarial Populations](https://mlsanity.com/paper/2008.01825/) (2020)
- [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)
- [Learning Control Policies for Stochastic Systems with Reach-avoid Guarantees](https://mlsanity.com/paper/2210.05308/) (2022)
- [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)
- [On the exact feasibility of convex scenario programs with discarded constraints](https://mlsanity.com/paper/2003.13433/) (2020)
- [StocHy: automated verification and synthesis of stochastic processes](https://mlsanity.com/paper/1901.10287/) (2019)
- [Sampling-Based Robust Control of Autonomous Systems with Non-Gaussian Noise](https://mlsanity.com/paper/2110.12662/) (2021)
- [Efficiency through Uncertainty: Scalable Formal Synthesis for Stochastic Hybrid Systems](https://mlsanity.com/paper/1901.01576/) (2019)
- [Probabilities Are Not Enough: Formal Controller Synthesis for Stochastic Dynamical Models with Epistemic Uncertainty](https://mlsanity.com/paper/2210.05989/) (2022)
- [Unified Multi-Rate Control: from Low Level Actuation to High Level Planning](https://mlsanity.com/paper/2012.06558/) (2020)
- [Scenario-Based Verification of Uncertain Parametric MDPs](https://mlsanity.com/paper/2112.13020/) (2021)
- [ProbReach: Verified Probabilistic Delta-Reachability for Stochastic Hybrid Systems](https://mlsanity.com/paper/1410.8060/) (2014)
- [Feedback Refinement Relations for the Synthesis of Symbolic Controllers](https://mlsanity.com/paper/1503.03715/) (2015)
- [Verification of general Markov decision processes by approximate similarity relations and policy refinement](https://mlsanity.com/paper/1605.09557/) (2016)
- [Correct-by-construction reach-avoid control of partially observable linear stochastic systems](https://mlsanity.com/paper/2103.02398/) (2021)
- [Sampling-Based Verification of CTMCs with Uncertain Rates](https://mlsanity.com/paper/2205.08300/) (2022)
- [Approximate Abstractions of Markov Chains with Interval Decision Processes (Extended Version)](https://mlsanity.com/paper/1804.08554/) (2018)

## Built on by (most cited first, 16 of 16)

- [Robust Markov Decision Processes: A Place Where AI and Formal Methods Meet](https://mlsanity.com/paper/2411.11451/) (2024)
- [Decision-Making Under Uncertainty: Beyond Probabilities](https://mlsanity.com/paper/2303.05848/) (2023)
- [Shielded Reinforcement Learning for Hybrid Systems](https://mlsanity.com/paper/2308.14424/) (2023)
- [What Are the Odds? Improving the foundations of Statistical Model Checking](https://mlsanity.com/paper/2404.05424/) (2024)
- [Bridging conformal prediction and scenario optimization](https://mlsanity.com/paper/2503.23561/) (2025)
- [Pick-to-Learn for Systems and Control: Data-driven Synthesis with State-of-the-art Safety Guarantees](https://mlsanity.com/paper/2512.04781/) (2025)
- [Policy Verification in Stochastic Dynamical Systems Using Logarithmic Neural Certificates](https://mlsanity.com/paper/2406.00826/) (2024)
- [Data-driven abstractions via adaptive refinements and a Kantorovich metric [extended version]](https://mlsanity.com/paper/2303.17618/) (2023)
- [Formally Verifying and Explaining Sepsis Treatment Policies with COOL-MC](https://mlsanity.com/paper/2602.14505/) (2026)
- [Composing Reinforcement Learning Policies, with Formal Guarantees](https://mlsanity.com/paper/2402.13785/) (2024)
- [Test Where Decisions Matter: Importance-driven Testing for Deep Reinforcement Learning](https://mlsanity.com/paper/2411.07700/) (2024)
- [Robust Shielding for Safe Reinforcement Learning](https://mlsanity.com/paper/2606.00270/) (2026)
- [Correct-by-Construction Control for Stochastic and Uncertain Dynamical Models via Formal Abstractions](https://mlsanity.com/paper/2311.09786/) (2023)
- [Neural Proofs for Sound Verification and Control of Complex Systems](https://mlsanity.com/paper/2512.18389/) (2025)
- [COOL-MC: Verifying and Explaining RL Policies for Platelet Inventory Management](https://mlsanity.com/paper/2603.02396/) (2026)
- [Clustered Randomized Smoothing for Stochastic Prediction Functions](https://mlsanity.com/paper/2608.12037/) (2026)

## Abstract (arXiv)

Controllers for dynamical systems that operate in safety-critical settings must account for stochastic disturbances. Such disturbances are often modeled as process noise in a dynamical system, 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 controller synthesis 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, while also avoiding unsafe regions of the state space. First, we abstract the continuous control system into a finite-state model that captures noise by probabilistic transitions between discrete 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, with a user-specified confidence probability, 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 original control system. In addition, we develop a tailored computational scheme that reduces the complexity of the synthesis of these guarantees on the iMDP. Benchmarks on realistic control systems show the practical applicability of our method, even when the iMDP has hundreds of millions of transitions.