论文标题
具有输入约束的控制 - 裂解和屏障函数的凸合成和验证
Convex synthesis and verification of control-Lyapunov and barrier functions with input constraints
论文作者
论文摘要
控制Lyapunov功能（CLF）和控制屏障功能（CBF）是广泛使用的工具，用于合成受稳定性和安全性约束的控制器。与在线优化相结合，它们提供了满足输入约束的稳定控制动作，并避免了状态空间的不安全区域。设计具有严格性能保证的CLF和CBF在计算上具有挑战性。为了证明控制动作的存在，当前技术不仅设计CLF/CBF，而且还设计了名义控制器。这可以使综合任务更加昂贵，并且性能估计更加保守。在这项工作中，我们使用平方符号条件来表征多项式CLFS/CBF，可以使用凸优化直接认证。这产生了不依赖标称控制器的CLF和CBF合成技术。然后，我们提出算法，以迭代地扩大可稳定和安全区域的估计。我们在2D玩具系统，摆锤和四型四型算法上演示了我们的算法。
Control Lyapunov functions (CLFs) and control barrier functions (CBFs) are widely used tools for synthesizing controllers subject to stability and safety constraints. Paired with online optimization, they provide stabilizing control actions that satisfy input constraints and avoid unsafe regions of state-space. Designing CLFs and CBFs with rigorous performance guarantees is computationally challenging. To certify existence of control actions, current techniques not only design a CLF/CBF, but also a nominal controller. This can make the synthesis task more expensive, and performance estimation more conservative. In this work, we characterize polynomial CLFs/CBFs using sum-of-squares conditions, which can be directly certified using convex optimization. This yields a CLF and CBF synthesis technique that does not rely on a nominal controller. We then present algorithms for iteratively enlarging estimates of the stabilizable and safe regions. We demonstrate our algorithms on a 2D toy system, a pendulum and a quadrotor.
