Probabilistic Safety Guarantee for Stochastic Control Systems Using Average Reward MDPs
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Abstract (arXiv)
Safety in stochastic control systems, which are subject to random noise with a known probability distribution, aims to compute policies that satisfy predefined operational constraints with high confidence throughout the uncertain evolution of the state variables. The unpredictable evolution of state variables poses a significant challenge for meeting predefined constraints using various control methods. To address this, we present a new algorithm that computes safe policies to determine the safety level across a finite state set. This algorithm reduces the safety objective to the standard average reward Markov Decision Process (MDP) objective. This reduction enables us to use standard techniques, such as linear programs, to compute and analyze safe policies. We validate the proposed method numerically on the Double Integrator and the Inverted Pendulum systems. Results indicate that the average-reward MDPs solution is more comprehensive, converges faster, and offers higher quality compared to the minimum discounted-reward solution.
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References · 12
- 2017A General Safety Framework for Learning-Based Control in Uncertain Robotic Systemscited by 163
- 2018A predictive safety filter for learning-based control of constrained nonlinear dynamical systemscited by 118
- 2017Robust Optimization for Non-Convex Objectivescited by 35
- 2022Control Barrier Functions and Input-to-State Safety with Application to Automated Vehiclescited by 13
- 2018A Minimum Discounted Reward Hamilton-Jacobi Formulation for Computing Reachable Setscited by 11
- 2024A Dynamic Safety Shield for Safe and Efficient Reinforcement Learning of Navigation Taskscited by 5
- 2023Safe Exploration in Reinforcement Learning: Training Backup Control Barrier Functions with Zero Training Time Safety Violationscited by 3
- 2025Back to Base: Towards Hands-Off Learning via Safe Resets with Reach-Avoid Safety Filterscited by 2
- 2018On reachability of Markov chains: A long-run average approachcited by 1
- 2024Data-Driven and Stealthy Deactivation of Safety Filterscited by 1
- 2024Learning for Layered Safety-Critical Control with Predictive Control Barrier Functionscited by 1
- 2025Control Barrier Functions for Shared Control and Vehicle Safetycited by 1
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