面向安全关键系统的鲁棒Taylor-Lagrange控制：保证可行性
Robust Taylor-Lagrange Control for Safety-Critical Systems with Guaranteed Feasibility
Wei Xiao, Christos Cassandras, Anni Li
AI 速览：提出鲁棒Taylor-Lagrange控制（rTLC），通过Taylor展开与Lagrange余项将安全函数展开到高于相对阶的阶数，以缓解离散化下的可行性保持问题并用于最优控制。
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.