# Safe Learning Control with Optimality and Stability Guarantees

arXiv: https://arxiv.org/abs/2501.15373 · HTML: https://mlsanity.com/paper/2501.15373/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Safe and constrained RL, one of 15 directions in Deep reinforcement learning methods.
- Builds on 14 of its 39 references that are in the map.
- First posted on arXiv 26 Jan 2025.

## Placed in

- Deep reinforcement learning methods / [Safe and constrained RL](https://mlsanity.com/deeprl/safe-and-constrained-rl/)

## Builds on (most cited first, 14 of 14)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Control Barrier Function Based Quadratic Programs for Safety Critical Systems](https://mlsanity.com/paper/1609.06408/) (2016)
- [Safe Reinforcement Learning Using Black-Box Reachability Analysis](https://mlsanity.com/paper/2204.07417/) (2022)
- [Balance Reward and Safety Optimization for Safe Reinforcement Learning: A Perspective of Gradient Manipulation](https://mlsanity.com/paper/2405.01677/) (2024)
- [Geometrically Constrained Trajectory Optimization for Multicopters](https://mlsanity.com/paper/2103.00190/) (2021)
- [Chance-Constrained Trajectory Optimization for Safe Exploration and Learning of Nonlinear Systems](https://mlsanity.com/paper/2005.04374/) (2020)
- [SafeLight: A Reinforcement Learning Method toward Collision-free Traffic Signal Control](https://mlsanity.com/paper/2211.10871/) (2022)
- [Safe Exploration in Model-based Reinforcement Learning using Control Barrier Functions](https://mlsanity.com/paper/2104.08171/) (2021)
- [High-order Barrier Functions: Robustness, Safety and Performance-Critical Control](https://mlsanity.com/paper/2104.00101/) (2021)
- [Safe Control Synthesis with Uncertain Dynamics and Constraints](https://mlsanity.com/paper/2202.09557/) (2022)
- [Robust Control Barrier Functions using Uncertainty Estimation with Application to Mobile Robots](https://mlsanity.com/paper/2401.01881/) (2024)
- [On the Optimality, Stability, and Feasibility of Control Barrier Functions: An Adaptive Learning-Based Approach](https://mlsanity.com/paper/2305.03608/) (2023)
- [Lagrangian-based online safe reinforcement learning for state-constrained systems](https://mlsanity.com/paper/2305.12967/) (2023)
- [HJB Based Optimal Safe Control Using Control Barrier Functions](https://mlsanity.com/paper/2106.15560/) (2021)

## Built on by (most cited first, 1 of 1)

- [Reinforcement learning in pursuit-evasion differential game: safety, stability and robustness](https://mlsanity.com/paper/2507.19516/) (2025)

## Abstract (arXiv)

Merely pursuing performance may adversely affect safety, while a conservative policy for safe exploration will degrade the performance. How to guarantee both safety and performance in learning-based control problems is an interesting yet challenging issue. This paper aims to enhance system performance with a safety guarantee by solving reinforcement learning (RL)-based optimal control problems for nonlinear systems subject to high-relative-degree state constraints and unknown time-varying disturbance/actuator faults. A new type of control barrier functions (CBFs), termed high-order reciprocal-based control barrier function, is proposed to handle high-relative-degree constraints, which extends the design of CBFs to enforce robust safety without knowing the disturbance bound. The concept of gradient similarity is proposed to quantify the relationship between safety and performance. Finally, gradient manipulation and adaptive mechanisms are introduced in the model-based safe RL framework to enhance the performance with a safety guarantee. Two simulation examples illustrate the efficacy of the proposed algorithms.