TY - JOUR
T1 - A Semialgebraic Framework for Verification and Synthesis of Control Barrier Functions
AU - Clark, Andrew
N1 - Publisher Copyright:
© 1963-2012 IEEE.
PY - 2025
Y1 - 2025
N2 - Safety is a critical property for control systems in medicine, transportation, manufacturing, and other applications, and can be defined as ensuring positive invariance of a predefined safe set. This article investigates the problems of verifying positive invariance of a semialgebraic set as well as synthesizing sets that can be made positive invariant through control barrier function (CBF)-based control. The key to our approach consists of mapping conditions for positive invariance to sum-of-squares constraints via the Positivstellensatz from real algebraic geometry. Based on these conditions, we propose a framework for verifying safety of CBF-based control including single CBFs, high-order CBFs, multi-CBFs, and systems with trigonometric dynamics and actuation constraints. In the area of synthesis, we propose algorithms for constructing CBFs, namely, an alternating-descent approach and a local CBF approach. We evaluate our approach through case studies on quadrotor UAV and power converter test systems.
AB - Safety is a critical property for control systems in medicine, transportation, manufacturing, and other applications, and can be defined as ensuring positive invariance of a predefined safe set. This article investigates the problems of verifying positive invariance of a semialgebraic set as well as synthesizing sets that can be made positive invariant through control barrier function (CBF)-based control. The key to our approach consists of mapping conditions for positive invariance to sum-of-squares constraints via the Positivstellensatz from real algebraic geometry. Based on these conditions, we propose a framework for verifying safety of CBF-based control including single CBFs, high-order CBFs, multi-CBFs, and systems with trigonometric dynamics and actuation constraints. In the area of synthesis, we propose algorithms for constructing CBFs, namely, an alternating-descent approach and a local CBF approach. We evaluate our approach through case studies on quadrotor UAV and power converter test systems.
KW - Control barrier function (CBF)
KW - safety
KW - sum-of-squares (SOS) optimization
UR - http://www.scopus.com/inward/record.url?scp=105003776171&partnerID=8YFLogxK
U2 - 10.1109/TAC.2024.3497001
DO - 10.1109/TAC.2024.3497001
M3 - Article
AN - SCOPUS:105003776171
SN - 0018-9286
VL - 70
SP - 3101
EP - 3116
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
IS - 5
ER -