mlsanityData to 14 Oct 2026

Safe Learning of Regions of Attraction for Uncertain, Nonlinear Systems with Gaussian Processes

arXiv 1603.04915 ↗First posted 15 Mar 2016eess.SY cs.SYcited by 39

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Abstract (arXiv)

Control theory can provide useful insights into the properties of controlled, dynamic systems. One important property of nonlinear systems is the region of attraction (ROA), a safe subset of the state space in which a given controller renders an equilibrium point asymptotically stable. The ROA is typically estimated based on a model of the system. However, since models are only an approximation of the real world, the resulting estimated safe region can contain states outside the ROA of the real system. This is not acceptable in safety-critical applications. In this paper, we consider an approach that learns the ROA from experiments on a real system, without ever leaving the true ROA and, thus, without risking safety-critical failures. Based on regularity assumptions on the model errors in terms of a Gaussian process prior, we use an underlying Lyapunov function in order to determine a region in which an equilibrium point is asymptotically stable with high probability. Moreover, we provide an algorithm to actively and safely explore the state space in order to expand the ROA estimate. We demonstrate the effectiveness of this method in simulation.

Key facts. Cited by 39 papers in the map (data through 14 Oct 2026). First posted on arXiv 15 Mar 2016.

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Citing papers per year: 2018: 1; 2019: 0; 2020: 0; 2021: 13; 2022: 9; 2023: 3; 2024: 7; 2025: 1; 2026: 5.

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  1. 2018EnsembleDAgger: A Bayesian Approach to Safe Imitation Learningcited by 100
  2. 2021Practical and Rigorous Uncertainty Bounds for Gaussian Process Regressioncited by 49
  3. 2022Neural Lyapunov Control of Unknown Nonlinear Systems with Stability Guaranteescited by 40
  4. 2023Physics-Informed Machine Learning for Modeling and Control of Dynamical Systemscited by 28
  5. 2021GoSafe: Globally Optimal Safe Robot Learningcited by 27
  6. 2021There Is No Turning Back: A Self-Supervised Approach for Reversibility-Aware Reinforcement Learningcited by 18
  7. 2022Safe Model-Based Reinforcement Learning with an Uncertainty-Aware Reachability Certificatecited by 18
  8. 2023A Human-Centered Safe Robot Reinforcement Learning Framework with Interactive Behaviorscited by 15
  9. 2021Model Error Propagation via Learned Contraction Metrics for Safe Feedback Motion Planning of Unknown Systemscited by 13
  10. 2021Pointwise Feasibility of Gaussian Process-based Safety-Critical Control under Model Uncertaintycited by 13
  11. 2022Statistical Safety and Robustness Guarantees for Feedback Motion Planning of Unknown Underactuated Stochastic Systemscited by 11
  12. 2021Learning the Koopman Eigendecomposition: A Diffeomorphic Approachcited by 9
27 more
  1. 2024Stability-informed Bayesian Optimization for MPC Cost Function Learningcited by 8
  2. 2024Learning Control Barrier Functions and their application in Reinforcement Learning: A Surveycited by 8
  3. 2021Uniform Error and Posterior Variance Bounds for Gaussian Process Regression with Application to Safe Controlcited by 7
  4. 2024Safe and Stable Closed-Loop Learning for Neural-Network-Supported Model Predictive Controlcited by 7
  5. 2026Safety Beyond the Training Data: Robust Out-of-Distribution MPC via Conformalized System Level Synthesiscited by 7
  6. 2022SAAC: Safe Reinforcement Learning as an Adversarial Game of Actor-Criticscited by 6
  7. 2022Effects of Safety State Augmentation on Safe Explorationcited by 6
  8. 2021Inverse Reinforcement Learning: A Control Lyapunov Approachcited by 5
  9. 2021Formal Verification of Unknown Dynamical Systems via Gaussian Process Regressioncited by 5
  10. 2022Physically Consistent Learning of Conservative Lagrangian Systems with Gaussian Processescited by 5
  11. 2023System-level Safety Guard: Safe Tracking Control through Uncertain Neural Network Dynamics Modelscited by 5
  12. 2021Lyapunov-based uncertainty-aware safe reinforcement learningcited by 3
  13. 2022Gaussian Control Barrier Functions : A Non-Parametric Paradigm to Safetycited by 2
  14. 2022Recursively Feasible Probabilistic Safe Online Learning with Control Barrier Functionscited by 2
  15. 2024Stochastic Reinforcement Learning with Stability Guarantees for Control of Unknown Nonlinear Systemscited by 2
  16. 2021OpReg-Boost: Learning to Accelerate Online Algorithms with Operator Regressioncited by 1
  17. 2021Learning To Estimate Regions Of Attraction Of Autonomous Dynamical Systems Using Physics-Informed Neural Networkscited by 1
  18. 2022Model-free Learning of Regions of Attraction via Recurrent Setscited by 1
  19. 2021Data Generation Method for Learning a Low-dimensional Safe Region in Safe Reinforcement Learningcited by 0
  20. 2024GenSafe: A Generalizable Safety Enhancer for Safe Reinforcement Learning Algorithms Based on Reduced Order Markov Decision Process Modelcited by 0
  21. 2024Improving the Region of Attraction of a Multi-rotor UAV by Estimating Unknown Disturbancescited by 0
  22. 2024Theoretical Analysis of Heteroscedastic Gaussian Processes with Posterior Distributionscited by 0
  23. 2025Lyapunov Stability Learning with Nonlinear Control via Inductive Biasescited by 0
  24. 2026On the Equilibrium between Feasible Zone and Uncertain Model in Safe Explorationcited by 0
  25. 2026Learning over Forward-Invariant Policy Classes: Reinforcement Learning without Safety Concernscited by 0
  26. 2026Hierarchical Causal Abduction: A Foundation Framework for Explainable Model Predictive Controlcited by 0
  27. 2026Proactive Context-Forecasted Safety Constraints for Nonstationary Reinforcement Learningcited by 0