# Real-time Safety Index Adaptation for Parameter-varying Systems via Determinant Gradient Ascend

arXiv: https://arxiv.org/abs/2403.14968 · HTML: https://mlsanity.com/paper/2403.14968/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Mar 2024.

## Built on by (most cited first, 4 of 4)

- [Implicit Safe Set Algorithm for Provably Safe Reinforcement Learning](https://mlsanity.com/paper/2405.02754/) (2024)
- [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)
- [Absolute State-wise Constrained Policy Optimization: High-Probability State-wise Constraints Satisfaction](https://mlsanity.com/paper/2410.01212/) (2024)

## Abstract (arXiv)

Safety Index Synthesis (SIS) is critical for deriving safe control laws. Recent works propose to synthesize a safety index (SI) via nonlinear programming and derive a safe control law such that the system 1) achieves forward invariant (FI) with some safe set and 2) guarantees finite time convergence (FTC) to that safe set. However, real-world system dynamics can vary during run-time, making the control law infeasible and invalidating the initial SI. Since the full SIS nonlinear programming is computationally expensive, it is infeasible to re-synthesize the SI each time the dynamics are perturbed. To address that, this paper proposes an efficient approach to adapting the SI to varying system dynamics and maintaining the feasibility of the safe control law. The proposed method leverages determinant gradient ascend and derives a closed-form update to safety index parameters, enabling real-time adaptation performance. A numerical study validates the effectiveness of our approach.