# Robust Taylor-Lagrange Control for Safety-Critical Systems

arXiv: https://arxiv.org/abs/2602.20076 · HTML: https://mlsanity.com/paper/2602.20076/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 27 references that are in the map.
- First posted on arXiv 23 Feb 2026.

## Builds on (most cited first, 8 of 8)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [End-to-End Safe Reinforcement Learning through Barrier Functions for Safety-Critical Continuous Control Tasks](https://mlsanity.com/paper/1903.08792/) (2019)
- [Control Barrier Function Based Quadratic Programs for Safety Critical Systems](https://mlsanity.com/paper/1609.06408/) (2016)
- [Adaptive Safety with Control Barrier Functions](https://mlsanity.com/paper/1910.00555/) (2019)
- [Control Barrier Functions for Stochastic Systems](https://mlsanity.com/paper/2003.03498/) (2020)
- [Control of Multi-Agent Systems with Finite Time Control Barrier Certificates and Temporal Logic](https://mlsanity.com/paper/1808.02393/) (2018)
- [Safety-Critical Event Triggered Control via Input-to-State Safe Barrier Functions](https://mlsanity.com/paper/2003.06963/) (2020)
- [Taylor-Lagrange Control for Safety-Critical Systems](https://mlsanity.com/paper/2512.11999/) (2025)

## Abstract (arXiv)

Solving safety-critical control problem has widely adopted the Control Barrier Function (CBF) method. However, the existence of a CBF is only a sufficient condition for system safety. The recently proposed Taylor-Lagrange Control (TLC) method addresses this limitation, but is vulnerable to the feasibility preservation problem (e.g., inter-sampling effect). In this paper, we propose a robust TLC (rTLC) method to address the feasibility preservation problem. Specifically, the rTLC method expands the safety function at an order higher than the relative degree of the function using Taylor's expansion with Lagrange remainder, which allows the control to explicitly show up at the current time instead of the future time in the TLC method. The rTLC method naturally addresses the feasibility preservation problem with only one hyper-parameter (the discretization time interval size during implementation), which is much less than its counterparts. Finally, we illustrate the effectiveness of the proposed rTLC method through an adaptive cruise control problem, and compare it with existing safety-critical control methods.