提升安全控制的可行性，解决采样间隔带来的失效问题。
Robust Taylor-Lagrange Control for Safety-Critical Systems
- 用泰勒-拉格朗日展开显式表达当前时刻控制量。
- 仅需一个超参数（离散化时间步长），避免未来控制依赖。
- 适用于自动驾驶等对安全性要求高的系统。
安全关键系统的控制常采用控制屏障函数（CBF）方法，但其存在性仅为系统安全的充分条件。近期提出的泰勒-拉格朗日控制（TLC）方法虽缓解此问题，却仍受可行性保持难题（如采样间效应）影响。本文提出鲁棒泰勒-拉格朗日控制（rTLC），通过将安全函数在高于其相对阶数的阶次上进行带拉格朗日余项的泰勒展开，使控制量在当前时刻显式呈现，而非未来时刻。该方法天然解决可行性保持问题，且仅需一个超参数（实现时的离散化时间间隔大小），远少于现有方法。通过自适应巡航控制案例验证了rTLC的有效性，并与现有安全控制方法进行了对比。
原文摘要 · Abstract (English)
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.
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