Discrete-Time Control Barrier Function: High-Order Case and Adaptive Case
本文提出了高阶离散时间控制障碍函数和自适应离散时间控制障碍函数，用于保证离散系统安全集的前向不变性，并通过优化问题结合控制李雅普诺夫函数设计安全控制器，自适应方法通过时变惩罚函数提高可行性，在三连杆机械臂系统上验证了有效性。
This article proposes the novel concepts of the high-order discrete-time control barrier function (CBF) and adaptive discrete-time CBF. The high-order discrete-time CBF is used to guarantee forward invariance of a safe set for discrete-time systems of high relative degree. An optimization problem is then established unifying high-order discrete-time CBFs with discrete-time control Lyapunov functions to yield a safe controller. To improve the feasibility of such optimization problems, the adaptive discrete-time CBF is designed, which can relax constraints on system control input through time-varying penalty functions. The effectiveness of the proposed methods in dealing with high relative degree constraints and improving feasibility is verified on the discrete-time system of a three-link manipulator.