Robust Taylor-Lagrange Control for Safety-Critical Systems

TL;DR

This paper introduces a robust Taylor-Lagrange Control (rTLC) method that enhances safety-critical control by addressing feasibility issues through higher-order Taylor expansion, demonstrated on adaptive cruise control.

Contribution

The paper proposes a novel rTLC method that explicitly incorporates control at the current time, reducing hyper-parameter complexity and improving safety guarantees in control systems.

Findings

rTLC effectively addresses feasibility preservation issues.

The method outperforms existing safety-critical control approaches.

Demonstrated success in adaptive cruise control scenario.

Abstract

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.