Robust Taylor-Lagrange Control for Safety-Critical Systems

2026-02-23

AI Summary

This work proposes robust Taylor-Lagrange control (rTLC) to address the limitations of existing safety-critical control methods, such as control barrier functions, which only provide sufficient conditions for safety. While Taylor-Lagrange control (TLC) improves upon this by enabling necessary and sufficient conditions, it remains susceptible to infeasibility under practical discrete-time sampling due to feasibility preservation issues. rTLC overcomes this challenge by incorporating a Taylor expansion with Lagrange remainder at an order higher than the relative degree of the safety function, thereby explicitly introducing the control input at the current time step and fundamentally mitigating sampling-induced infeasibility. The approach requires tuning only a single hyperparameter—the discrete time step—greatly simplifying implementation. In adaptive cruise control scenarios, rTLC demonstrates superior robustness and feasibility preservation compared to existing methods.

Technology Category

• Intelligent Robots: Behavior Learning & Control
• Natural Language Processing: Safety and Robustness
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Search and Retrieval-Augmented AI: Agentic search
• Security and Privacy: Large-scale security measurements

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.

Problem

• safety-critical systems
• feasibility preservation problem
• Taylor-Lagrange Control
• Control Barrier Function
• inter-sampling effect

Innovation

• Robust Taylor-Lagrange Control
• Control Barrier Function
• Feasibility Preservation
• Safety-Critical Systems
• Taylor Expansion with Lagrange Remainder