Adaptive Control Barrier Functions

doi:10.1109/TAC.2021.3074895

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Adaptive Control Barrier Functions

2022-05-01

Wei Xiao *

Călin Belta

Christos G. Cassandras

DOI：10.1109/TAC.2021.3074895

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Abstract

En 中文

It has been shown that optimizing quadratic costs while stabilizing affine control systems to desired (sets of) states subject to state and control constraints can be reduced to a sequence of quadratic programs (QPs) by using control barrier functions (CBFs) and control Lyapunov functions (CLFs). In this article, we introduce adaptive CBFs (aCBFs) that can accommodate time-varying control bounds and noise in the system dynamics while also guaranteeing the feasibility of the QPs if the original quadratic cost optimization problem itself is feasible, which is a challenging problem in current approaches. We propose two different types of aCBFs: parameter-adaptive CBF (PACBF) and relaxation-adaptive CBF (RACBF). Central to aCBFs is the introduction of appropriate time-varying functions to modify the definition of a common CBF. These time-varying functions are treated as high-order CBFs with their own auxiliary dynamics, which are stabilized by CLFs. We demonstrate the advantages of using aCBFs over the existing CBF techniques by applying both the PACBF-based method and the RACBF-based method to a cruise control problem with time-varying road conditions and noise in the system dynamics, and compare their relative performance.

Keywords:

Adaptive systems

Time-varying systems

Safety

Optimal control

Uncertain systems

System dynamics

Noise measurement

Control barrier function (CBF)

Lyapunov methods

optimal control

safety-critical control

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