Constrained control of input-output linearizable systems using control sharing barrier functions

Control barrier functions (CBFs) have been used as an effective tool for designing a family of controls that ensures the forward invariance of a set. When multiple CBFs are present, it is important that the set of controls satisfying all the barrier conditions is non-empty. In this paper, we investigate such a control-sharing property for multiple CBFs and provide sufficient and necessary conditions for the property to hold. Based on that, we study the tracking control design problem of an input-output linearizable system with multiple time-varying output constraints, where the output constraints are encoded as CBFs and the barrier conditions are expressed as hard constraints in a quadratic program (QP) whose feasibility is guaranteed by the control-sharing property of the CBFs. With the controller generated from the QP, the output constraints are always satisfied and the tracking objective is achieved when it is not conflicting with the constraints. The effectiveness of our control design method is illustrated by two examples.