2019/03/12 by Wei Xiao, Xiao, Wei, Călin Belta +1 · 12 citations
Engineering · #Adaptive Control of Nonlinear Systems #Advanced Control Systems Optimization #FOS: Computer and information sciences #FOS: Electrical engineering #Robotics (cs.RO) #Stability and Control of Uncertain Systems #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1903.04706
openalex publication_date 2019/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper extends control barrier functions (CBFs) to high order control barrier functions (HOCBFs) that can be used for high relative degree constraints. The proposed HOCBFs are more general than recently proposed (exponential) HOCBFs. We introduce high order barrier functions (HOBF), and show that their satisfaction of Lyapunov-like conditions implies the forward invariance of the intersection of a series of sets. We then introduce HOCBF, and show that any control input that satisfies the HOCBF constraints renders the intersection of a series of sets forward invariant. We formulate optimal control problems with constraints given by HOCBF and control Lyapunov functions (CLF) and analyze the influence of the choice of the class K functions used in the definition of the HOCBF on the size of the feasible control region. We also provide a promising method to address the conflict between HOCBF constraints and control limitations by penalizing the class K functions. We illustrate the proposed method on an adaptive cruise control problem.