This article introduces the Pareto Control Barrier Function (PCBF) algorithm to maximize the inner safe set of dynamical systems under input constraints. Traditional Control Barrier Functions (CBFs) ensure safety by maintaining system trajectories within a safe set but often fail to account for realistic input constraints. To address this problem, we leverage the Pareto multi-task learning framework to balance competing objectives of safety and safe set volume. The PCBF algorithm is applicable to high-dimensional systems and is computationally efficient. We validate its effectiveness through comparison with Hamilton-Jacobi reachability for an inverted pendulum and through simulations on a 12-dimensional quadrotor system. Results show that the PCBF consistently outperforms existing methods, yielding larger safe sets and ensuring safety under input constraints.

翻译：本文提出帕累托控制屏障函数（PCBF）算法，用于在输入约束条件下最大化动态系统的内部安全集。传统控制屏障函数（CBF）通过将系统轨迹维持在安全集内来确保安全性，但往往未能考虑实际的输入约束。为解决该问题，我们利用帕累托多任务学习框架来平衡安全性目标与安全集体积目标之间的竞争关系。PCBF算法适用于高维系统且计算效率高。我们通过倒立摆系统与哈密顿-雅可比可达性分析的对比验证，以及12维四旋翼系统的仿真实验，证明了该算法的有效性。结果表明，PCBF算法在输入约束下始终优于现有方法，能够获得更大的安全集并确保系统安全性。