Deadlock Avoidance and Solution Time Optimization for Discrete-Time Control Systems via Control Barrier Functions

Safety is a critical component for dynamic systems. Simultaneously imposing multiple dynamic constraints on the dynamic systems for safety adjustment is a challenging problem. In recent years, control barrier functions (CBFs) have been proposed to deal with the safety problem of dynamic systems. In general, CBFs are combined with control Lyapunov functions (CLFs) by quadratic programming (QP) to construct optimal controller to guarantee the safe trajectory tracking of dynamic systems. In this paper, an augmented CBF is proposed to guarantee the safety of a class of discrete-time control systems. Also, control input perturbation (CIP) algorithm is provided to solve the deadlock problem. Additionally, in order to improve the efficiency of solving QP, switching control is used to reduce the solution time of QP greatly. Finally, the effectiveness of the proposed methods is verified by adjusting the set point of the 3D double integral (3DDI) dynamic system.