Control sharing barrier functions with application to constrained control

This paper investigates the control sharing property of two control barrier functions (CBFs), and its application to the control of strict feedback nonlinear systems with time-varying bounding output constraints. CBFs are used to design a family of controls that ensure the forward invariance of a set, which represents satisfaction of a safety specification. We call two CBFs have the control sharing property if a common control exists such that the two safety constraints can be satisfied simultaneously. A sufficient condition for the control sharing property is provided, and based on that, a control design method is given to the control of strict feedback nonlinear systems with time-varying output constraints. The effectiveness of the control design method is illustrated by an example.