mlsanityData to 7 Oct 2026

Safe Optimal Control Using Stochastic Barrier Functions and Deep Forward-Backward SDEs

arXiv 2009.01196 ↗First posted 2 Sep 2020eess.SY cs.AI cs.ROcited by 22

Not on the map. Why?

Abstract (arXiv)

This paper introduces a new formulation for stochastic optimal control and stochastic dynamic optimization that ensures safety with respect to state and control constraints. The proposed methodology brings together concepts such as Forward-Backward Stochastic Differential Equations, Stochastic Barrier Functions, Differentiable Convex Optimization and Deep Learning. Using the aforementioned concepts, a Neural Network architecture is designed for safe trajectory optimization in which learning can be performed in an end-to-end fashion. Simulations are performed on three systems to show the efficacy of the proposed methodology.

Key facts. Cited by 22 papers in the map (data through 7 Oct 2026). First posted on arXiv 2 Sep 2020.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 5; 2022: 5; 2023: 3; 2024: 4; 2025: 2; 2026: 3.

22 papers.

Sort:

By area:

  1. 2023SafeDiffuser: Safe Planning with Diffusion Probabilistic Modelscited by 69
  2. 2021Value Iteration in Continuous Actions, States and Timecited by 17
  3. 2024Constrained Reinforcement Learning with Smoothed Log Barrier Functioncited by 12
  4. 2021BarrierNet: A Safety-Guaranteed Layer for Neural Networkscited by 11
  5. 2022Probabilities Are Not Enough: Formal Controller Synthesis for Stochastic Dynamical Models with Epistemic Uncertaintycited by 11
  6. 2022Differentiable Control Barrier Functions for Vision-based End-to-End Autonomous Drivingcited by 10
  7. 2022On the Forward Invariance of Neural ODEscited by 10
  8. 2023Benchmarking Actor-Critic Deep Reinforcement Learning Algorithms for Robotics Control with Action Constraintscited by 10
  9. 2021Robust Value Iteration for Continuous Control Taskscited by 8
  10. 2022Differentiable Safe Controller Design through Control Barrier Functionscited by 8
  11. 2025Discrete GCBF Proximal Policy Optimization for Multi-agent Safe Optimal Controlcited by 7
  12. 2021Continuous-Time Fitted Value Iteration for Robust Policiescited by 6
10 more
  1. 2023A Generalizable Physics-informed Learning Framework for Risk Probability Estimationcited by 4
  2. 2025Hierarchical Multi-Agent Reinforcement Learning with Control Barrier Functions for Safety-Critical Autonomous Systemscited by 4
  3. 2022Decentralized Safe Multi-agent Stochastic Optimal Control using Deep FBSDEs and ADMMcited by 3
  4. 2024Myopically Verifiable Probabilistic Certificates for Safe Control and Learningcited by 1
  5. 2024Generalizable Physics-Informed Learning for Stochastic Safety-Critical Systemscited by 1
  6. 2026PoSafeNet: Safe Learning with Poset-Structured Neural Netscited by 1
  7. 2021Deep L1 Stochastic Optimal Control Policies for Planetary Soft-landingcited by 0
  8. 2024ABNet: Attention BarrierNet for Safe and Scalable Robot Learningcited by 0
  9. 2026BarrierSteer: LLM Safety via Learning Barrier Steeringcited by 0
  10. 2026Safe and Generalizable Hierarchical Multi-Agent RL via Constraint Manifold Controlcited by 0