The effect of control barrier functions on energy transfers in controlled physical systems

TL;DR

This paper investigates how control barrier functions influence energy transfer in controlled physical systems using port-Hamiltonian formalism, offering new tools for designing safety-critical controls that shape energetic behaviors.

Contribution

It introduces a novel analysis framework linking control barrier functions with energy transfer, enabling the design of controls that induce specific energetic effects in physical systems.

Findings

CBFs can induce damping and energy injection effects

The framework allows for designing CBFs to control energy transfer

Simulations validate the theoretical predictions

Abstract

Using a port-Hamiltonian formalism, we show the qualitative and quantitative effect of safety-critical control implemented with control barrier functions (CBFs) on the power balance of controlled physical systems. The presented results will provide novel tools to design CBFs inducing desired energetic behaviors of the closed-loop system, including nontrivial damping injection effects and non-passive control actions, effectively injecting energy in the system in a controlled manner. Simulations validate the stated results.