面向安全关键系统的鲁棒 Taylor-Lagrange 控制（rTLC）方法：保证可行性
Robust Taylor-Lagrange Control for Safety-Critical Systems with Guaranteed Feasibility
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研究者提出鲁棒 Taylor-Lagrange 控制（rTLC）方法，解决 TLC 方法在时间离散化下的可行性保持问题。该方法利用带 Lagrange 余项的 Taylor 展开将安全函数展开到高于相对阶一阶，使控制量在当前时刻显式出现，保证整个离散化时间区间内安全约束得到满足，且仅需一个超参数（离散化时间区间大小）。自适应巡航控制实验验证了其有效性。
正文 · 原文
Abstract:The Control Barrier Function (CBF) method has been widely adopted in solving safety-critical control problems. 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 by providing a necessary and sufficient condition, but it is still vulnerable to the feasibility preservation problem (e.g., due to the inter-sampling effect when time is discretized). In this paper, we propose a robust TLC (rTLC) method to address the feasibility preservation problem and show how to use it to solve optimal control problems. Specifically, the rTLC method expands the safety function to an order higher than its relative degree using Taylor's expansion with Lagrange remainder, which allows the control to explicitly show up at the current time instead of a future time in the original TLC method. This implies that the safety constraint remains satisfied over the entire discretization time interval that follows. Moreover, the rTLC method naturally addresses the feasibility preservation problem with only a single hyper-parameter (the discretization time interval size during implementation), compared to significantly more parameters for 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.
| Comments: | This version addressed one technical problem of the inter-sampling effect in rTLC |
| Subjects: | Systems and Control (eess.SY); Artificial Intelligence (cs.AI); Robotics (cs.RO) |
| Cite as: | arXiv:2602.20076 [eess.SY] |
| (or arXiv:2602.20076v2 [eess.SY] for this version) | |
| https://doi.org/10.48550/arXiv.2602.20076 arXiv-issued DOI via DataCite |
Submission history
From: Wei Xiao [view email]
[v1]
Mon, 23 Feb 2026 17:40:05 UTC (163 KB)
[v2]
Thu, 29 Oct 2026 16:16:00 UTC (164 KB)
来源：arXiv cs.AI · arxiv.org