# Persistently Feasible Robust Safe Control by Safety Index Synthesis and Convex Semi-Infinite Programming

arXiv: https://arxiv.org/abs/2209.06896 · HTML: https://mlsanity.com/paper/2209.06896/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Sep 2022.

## Built on by (most cited first, 12 of 12)

- [State-wise Safe Reinforcement Learning: A Survey](https://mlsanity.com/paper/2302.03122/) (2023)
- [GUARD: A Safe Reinforcement Learning Benchmark](https://mlsanity.com/paper/2305.13681/) (2023)
- [State-wise Constrained Policy Optimization](https://mlsanity.com/paper/2306.12594/) (2023)
- [Verified Safe Reinforcement Learning for Neural Network Dynamic Models](https://mlsanity.com/paper/2405.15994/) (2024)
- [Learning Predictive Safety Filter via Decomposition of Robust Invariant Set](https://mlsanity.com/paper/2311.06769/) (2023)
- [Implicit Safe Set Algorithm for Provably Safe Reinforcement Learning](https://mlsanity.com/paper/2405.02754/) (2024)
- [Absolute Policy Optimization](https://mlsanity.com/paper/2310.13230/) (2023)
- [Meta-Control: Automatic Model-based Control Synthesis for Heterogeneous Robot Skills](https://mlsanity.com/paper/2405.11380/) (2024)
- [The Feasibility Theory of Constrained Reinforcement Learning: A Tutorial Study](https://mlsanity.com/paper/2404.10064/) (2024)
- [Safe PDE Boundary Control with Neural Operators](https://mlsanity.com/paper/2411.15643/) (2024)
- [Absolute State-wise Constrained Policy Optimization: High-Probability State-wise Constraints Satisfaction](https://mlsanity.com/paper/2410.01212/) (2024)
- [Control Invariant Sets for Neural Network Dynamical Systems and Recursive Feasibility in Model Predictive Control](https://mlsanity.com/paper/2505.11546/) (2025)

## Abstract (arXiv)

Model mismatches prevail in real-world applications. Ensuring safety for systems with uncertain dynamic models is critical. However, existing robust safe controllers may not be realizable when control limits exist. And existing methods use loose over-approximation of uncertainties, leading to conservative safe controls. To address these challenges, we propose a control-limits aware robust safe control framework for bounded state-dependent uncertainties. We propose safety index synthesis to find a robust safe controller guaranteed to be realizable under control limits. And we solve for robust safe control via Convex Semi-Infinite Programming, which is the tightest formulation for convex bounded uncertainties and leads to the least conservative control. In addition, we analyze when and how safety can be preserved under unmodeled uncertainties. Experiment results show that our robust safe controller is always realizable under control limits and is much less conservative than strong baselines.