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.

翻译：解决安全关键控制问题已广泛采用控制屏障函数（CBF）方法。然而，CBF的存在仅是系统安全的充分条件。最近提出的泰勒-拉格朗日控制（TLC）方法解决了这一局限性，但易受可行性保持问题（例如采样间效应）的影响。本文提出一种鲁棒TLC（rTLC）方法以解决可行性保持问题。具体而言，rTLC方法使用带拉格朗日余项的泰勒展开，将安全函数展开至高于该函数相对阶数的阶次，这使得控制量能在当前时刻显式出现，而非如TLC方法中出现在未来时刻。rTLC方法仅需一个超参数（实现时的离散时间间隔大小）即可自然解决可行性保持问题，其数量远少于同类方法。最后，我们通过自适应巡航控制问题说明了所提rTLC方法的有效性，并与现有安全关键控制方法进行了比较。