Self-triggered Control for Safety Critical Systems using Control Barrier Functions

TL;DR

This paper introduces a real-time self-triggered control method combining CLF and CBF with a ZOH implementation, ensuring safety and avoiding unnecessary updates in safety-critical systems.

Contribution

It presents a novel self-triggered control strategy using a ZOH approach and introduces the concept of safe period to guarantee safety and prevent Zeno behavior.

Findings

Ensures safety constraints with fewer controller updates.

Proves absence of Zeno behavior near equilibrium.

Demonstrates improved efficiency over periodic control methods.

Abstract

We propose a real-time control strategy that combines self-triggered control with Control Lyapunov Functions (CLF) and Control Barrier Functions (CBF). Similar to related works proposing CLF-CBF-based controllers, the computation of the controller is achieved by solving a Quadratic Program (QP). However, we propose a Zeroth-Order Hold (ZOH) implementation of the controller that overcomes the main limitations of traditional approaches based on periodic controllers, i.e., unnecessary controller updates and potential violations of the safety constraints. Central to our approach is the novel notion of safe period, which enforces a strong safety guarantee for implementing ZOH control. In addition, we prove that the system does not exhibit a Zeno behavior as it approaches the desired equilibrium.