mlsanityData to 7 Oct 2026

Safe Control with Neural Network Dynamic Models

arXiv 2110.01110 ↗First posted 3 Oct 2021cs.RO cs.LG cs.SYcited by 21

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Abstract (arXiv)

Safety is critical in autonomous robotic systems. A safe control law ensures forward invariance of a safe set (a subset in the state space). It has been extensively studied regarding how to derive a safe control law with a control-affine analytical dynamic model. However, in complex environments and tasks, it is challenging and time-consuming to obtain a principled analytical model of the system. In these situations, data-driven learning is extensively used and the learned models are encoded in neural networks. How to formally derive a safe control law with Neural Network Dynamic Models (NNDM) remains unclear due to the lack of computationally tractable methods to deal with these black-box functions. In fact, even finding the control that minimizes an objective for NNDM without any safety constraint is still challenging. In this work, we propose MIND-SIS (Mixed Integer for Neural network Dynamic model with Safety Index Synthesis), the first method to derive safe control laws for NNDM. The method includes two parts: 1) SIS: an algorithm for the offline synthesis of the safety index (also called as barrier function), which uses evolutionary methods and 2) MIND: an algorithm for online computation of the optimal and safe control signal, which solves a constrained optimization using a computationally efficient encoding of neural networks. It has been theoretically proved that MIND-SIS guarantees forward invariance and finite convergence. And it has been numerically validated that MIND-SIS achieves safe and optimal control of NNDM. From our experiments, the optimality gap is less than 10-8, and the safety constraint violation is 0.

Key facts. Cited by 21 papers in the map (data through 7 Oct 2026). Builds on 16 of its 36 references that are in the map. First posted on arXiv 3 Oct 2021.

Builds on

16 of 36 references.

References · 16

  1. 2019When to Trust Your Model: Model-Based Policy Optimizationcited by 753
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  5. 2017Neural Network Dynamics for Model-Based Deep Reinforcement Learning with Model-Free Fine-Tuningcited by 288
  6. 2016Control Barrier Function Based Quadratic Programs for Safety Critical Systemscited by 261
  7. 2017Formal Verification of Piece-Wise Linear Feed-Forward Neural Networkscited by 241
  8. 2019Algorithms for Verifying Deep Neural Networkscited by 221
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  12. 2018A Dual Approach to Scalable Verification of Deep Networkscited by 125
4 more
  1. 2020Enabling certification of verification-agnostic networks via memory-efficient semidefinite programmingcited by 65
  2. 2019Safe Control Algorithms Using Energy Functions: A Unified Framework, Benchmark, and New Directionscited by 17
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 2; 2023: 7; 2024: 7; 2025: 4; 2026: 1.

21 papers.

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  1. 2023State-wise Safe Reinforcement Learning: A Surveycited by 48
  2. 2022Safe Control Under Input Limits with Neural Control Barrier Functionscited by 27
  3. 2025Steering Dialogue Dynamics for Robustness against Multi-turn Jailbreaking Attackscited by 20
  4. 2023Model-Based Control with Sparse Neural Dynamicscited by 16
  5. 2024Verification of Neural Control Barrier Functions with Symbolic Derivative Bounds Propagationcited by 12
  6. 2023Adversarial Robustness Certification for Bayesian Neural Networkscited by 7
  7. 2024Verified Safe Reinforcement Learning for Neural Network Dynamic Modelscited by 7
  8. 2024ModelVerification.jl: a Comprehensive Toolbox for Formally Verifying Deep Neural Networkscited by 7
  9. 2022Reachable Polyhedral Marching (RPM): An Exact Analysis Tool for Deep-Learned Control Systemscited by 6
  10. 2023System-level Safety Guard: Safe Tracking Control through Uncertain Neural Network Dynamics Modelscited by 5
  11. 2024Real-Time Safe Control of Neural Network Dynamic Models with Sound Approximationcited by 5
  12. 2023Promises of Deep Kernel Learning for Control Synthesiscited by 4
9 more
  1. 2023Probabilistic Reach-Avoid for Bayesian Neural Networkscited by 4
  2. 2023Efficient Certified Training and Robustness Verification of Neural ODEscited by 3
  3. 2024Meta-Control: Automatic Model-based Control Synthesis for Heterogeneous Robot Skillscited by 2
  4. 2024Myopically Verifiable Probabilistic Certificates for Safe Control and Learningcited by 1
  5. 2025ECLipsE-Gen-Local: Efficient Compositional Local Lipschitz Estimates for Deep Neural Networkscited by 1
  6. 2026Dyna-Style Safety Augmented Reinforcement Learning: Staying Safe in the Face of Uncertaintycited by 1
  7. 2024Efficient model predictive control for nonlinear systems modelled by deep neural networkscited by 0
  8. 2025Safe Beyond the Horizon: Efficient Sampling-based MPC with Neural Control Barrier Functionscited by 0
  9. 2025Control Invariant Sets for Neural Network Dynamical Systems and Recursive Feasibility in Model Predictive Controlcited by 0