mlsanityData to 14 Oct 2026

Imitation Learning with Stability and Safety Guarantees

arXiv 2012.09293 ↗First posted 16 Dec 2020eess.SY cs.SYcited by 34

On the map: Offline RL and imitation learning from data → Imitation learning methods

Abstract (arXiv)

A method is presented to learn neural network (NN) controllers with stability and safety guarantees through imitation learning (IL). Convex stability and safety conditions are derived for linear time-invariant plant dynamics with NN controllers by merging Lyapunov theory with local quadratic constraints to bound the nonlinear activation functions in the NN. These conditions are incorporated in the IL process, which minimizes the IL loss, and maximizes the volume of the region of attraction associated with the NN controller simultaneously. An alternating direction method of multipliers based algorithm is proposed to solve the IL problem. The method is illustrated on an inverted pendulum system, aircraft longitudinal dynamics, and vehicle lateral dynamics.

Key facts. Cited by 34 papers in the map (data through 14 Oct 2026). Placed in Imitation learning methods, one of 13 directions in Offline RL and imitation learning from data. Builds on 19 of its 33 references that are in the map. First posted on arXiv 16 Dec 2020.

Builds on

19 of 33 references.

Closest ancestors · 1

Same direction, newest first

  1. 2018An Algorithmic Perspective on Imitation Learning16 Nov

Other references · 18

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2018On the Effectiveness of Interval Bound Propagation for Training Verifiably Robust Modelscited by 328
  3. 2019Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networkscited by 293
  4. 2017A General Safety Framework for Learning-Based Control in Uncertain Robotic Systemscited by 163
  5. 2019Safety Verification and Robustness Analysis of Neural Networks via Quadratic Constraints and Semidefinite Programmingcited by 101
  6. 2020Training robust neural networks using Lipschitz boundscited by 99
  7. 2015Global Convergence of ADMM in Nonconvex Nonsmooth Optimizationcited by 98
  8. 2017Deeply AggreVaTeD: Differentiable Imitation Learning for Sequential Predictioncited by 93
  9. 2018Efficient representation and approximation of model predictive control laws via deep learningcited by 58
  10. 2020Stability Analysis using Quadratic Constraints for Systems with Neural Network Controllerscited by 44
  11. 2020Reach-SDP: Reachability Analysis of Closed-Loop Systems with Neural Network Controllers via Semidefinite Programmingcited by 43
  12. 2020Enforcing robust control guarantees within neural network policiescited by 40
6 more
  1. 2018Stability-certified reinforcement learning: A control-theoretic perspectivecited by 31
  2. 2020Learning Hybrid Control Barrier Functions from Datacited by 24
  3. 2019Safe and Near-Optimal Policy Learning for Model Predictive Control using Primal-Dual Neural Networkscited by 13
  4. 2020Offset-free setpoint tracking using neural network controllerscited by 10
  5. 2020A Control Barrier Perspective on Episodic Learning via Projection-to-State Safetycited by 7
  6. 2020A Convex Parameterization of Robust Recurrent Neural Networkscited by 2

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2020: 1; 2021: 9; 2022: 9; 2023: 5; 2024: 3; 2025: 5; 2026: 2.

34 papers.

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  1. 2021Recurrent Equilibrium Networks: Flexible Dynamic Models with Guaranteed Stability and Robustnesscited by 45
  2. 2021On the Sample Complexity of Stability Constrained Imitation Learningcited by 38
  3. 2022TaSIL: Taylor Series Imitation Learningcited by 21
  4. 2021Learning Robust Output Control Barrier Functions from Safe Expert Demonstrationscited by 20
  5. 2021Recurrent Neural Network Controllers Synthesis with Stability Guarantees for Partially Observed Systemscited by 16
  6. 2020Synthesizing Decentralized Controllers with Graph Neural Networks and Imitation Learningcited by 12
  7. 2023CCIL: Context-conditioned imitation learning for urban drivingcited by 12
  8. 2022Neural network training under semidefinite constraintscited by 11
  9. 2021On Imitation Learning of Linear Control Policies: Enforcing Stability and Robustness Constraints via LMI Conditionscited by 10
  10. 2022End-to-End Imitation Learning with Safety Guarantees using Control Barrier Functionscited by 10
  11. 2021Robustness against Adversarial Attacks in Neural Networks using Incremental Dissipativitycited by 7
  12. 2022Towards a Theoretical Foundation of Policy Optimization for Learning Control Policiescited by 6
22 more
  1. 2023Convolutional Neural Networks as 2-D systemscited by 5
  2. 2024RAIL: Reachability-Aided Imitation Learning for Safe Policy Executioncited by 5
  3. 2023Initial State Interventions for Deconfounded Imitation Learningcited by 4
  4. 2024Ensuring Both Positivity and Stability Using Sector-Bounded Nonlinearity for Systems with Neural Network Controllerscited by 4
  5. 2022Learning Neural Networks under Input-Output Specificationscited by 3
  6. 2024Transformer-Based Fault-Tolerant Control for Fixed-Wing UAVs Using Knowledge Distillation and In-Context Adaptationcited by 3
  7. 2021Learning to Act Safely with Limited Exposure and Almost Sure Certaintycited by 2
  8. 2021Imitation Learning of Stabilizing Policies for Nonlinear Systemscited by 2
  9. 2022Fail-Safe Adversarial Generative Imitation Learningcited by 2
  10. 2025Robust Stability Analysis of Positive Lure System with Neural Network Feedbackcited by 2
  11. 2025Local Stability and Region of Attraction Analysis for Neural Network Feedback Systems under Positivity Constraintscited by 2
  12. 2021Robust Stability of Neural Network-controlled Nonlinear Systems with Parametric Variabilitycited by 1
  13. 2022Dissipative Imitation Learning for Robust Dynamic Output Feedbackcited by 1
  14. 2025Distributionally Robust Imitation Learning: Layered Control Architecture for Certifiable Autonomycited by 1
  15. 2026Bridging Control with Neural Network Verifier alpha-beta-CROWN: A Tutorialcited by 1
  16. 2022Cross apprenticeship learning framework: Properties and solution approachescited by 0
  17. 2022Follow the Clairvoyant: an Imitation Learning Approach to Optimal Controlcited by 0
  18. 2023Rational Neural Network Controllerscited by 0
  19. 2023Dissipative Imitation Learning for Discrete Dynamic Output Feedback Control with Sparse Data Setscited by 0
  20. 2025A Scalable Approach for Safe and Robust Learning via Lipschitz-Constrained Networkscited by 0
  21. 2025Towards Safe Imitation Learning via Potential Field-Guided Flow Matchingcited by 0
  22. 2026Infeasible optimization problems and the hierarchical augmented Lagrangian method in imitation learningcited by 0

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  1. 2025Imitation Learning of MPC with Neural Networks: Error Guarantees and Sparsification
  2. 2024Globally Stable Neural Imitation Policies
  3. 2023Learning Lyapunov-Stable Polynomial Dynamical Systems through Imitation
  4. 2026Stability-Aware Imitation Learning from Model Predictive Control for Autonomous Vehicle Lateral Control: Exact Q-Loss and a Novel Training Procedure
  5. 2022Generating Stable and Collision-Free Policies through Lyapunov Function Learning
  6. 2024Fusion Dynamical Systems with Machine Learning in Imitation Learning: A Comprehensive Overview
  7. 2026Interleaved Projected Gradient Descent for Safe Imitation Learning
  8. 2024Verified Safe Reinforcement Learning for Neural Network Dynamic Models