# Safe Adaptation with Multiplicative Uncertainties Using Robust Safe Set Algorithm

arXiv: https://arxiv.org/abs/1912.09095 · HTML: https://mlsanity.com/paper/1912.09095/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Dec 2019.

## Built on by (most cited first, 8 of 8)

- [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)
- [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)
- [Absolute State-wise Constrained Policy Optimization: High-Probability State-wise Constraints Satisfaction](https://mlsanity.com/paper/2410.01212/) (2024)
- [Safety Reinforced Model Predictive Control (SRMPC): Improving MPC with Reinforcement Learning for Motion Planning in Autonomous Driving](https://mlsanity.com/paper/2512.03774/) (2025)

## Abstract (arXiv)

Maintaining safety under adaptation has long been considered to be an important capability for autonomous systems. As these systems estimate and change the ego-model of the system dynamics, questions regarding how to develop safety guarantees for such systems continue to be of interest. We propose a novel robust safe control methodology that uses set-based safety constraints to make a robotic system with dynamical uncertainties safely adapt and operate in its environment. The method consists of designing a scalar energy function (safety index) for an adaptive system with parametric uncertainty and an optimization-based approach for control synthesis. Simulation studies on a two-link manipulator are conducted and the results demonstrate the effectiveness of our proposed method in terms of generating provably safe control for adaptive systems with parametric uncertainty.