提出闭式解方法，让受限输入系统实时安全控制更高效。
Safety-Critical Control with Bounded Inputs: A Closed-Form Solution for Backup Control Barrier Functions
- 通过最优插值融合主控制器与备用控制器。
- 推导出运行时无需求解优化问题的闭式解。
- 在飞行器等计算资源受限场景中验证有效。
验证控制器安全性对诸多应用至关重要，尤其对输入受限的系统更具挑战性。备份控制屏障函数（bCBFs）通过利用备用控制器的知识，提供了一种结构化方法来合成满足输入约束的安全控制器。然而，传统bCBFs需在运行时求解高维二次规划，对计算资源受限的系统（如航空航天器）而言代价过高。本文提出一种最优插值方法，在主控制器与备用控制器间进行平滑过渡，并推导出该优化问题的闭式解。理论证明该闭式控制器可保证系统安全且严格遵守输入约束。在双积分器和非线性固定翼飞机实例上验证了方法的有效性。
原文摘要 · Abstract (English)
Verifying the safety of controllers is critical for many applications, but is especially challenging for systems with bounded inputs. Backup control barrier functions (bCBFs) offer a structured approach to synthesizing safe controllers that are guaranteed to satisfy input bounds by leveraging the knowledge of a backup controller. While powerful, bCBFs require solving a high-dimensional quadratic program at run-time, which may be too costly for computationally-constrained systems such as aerospace vehicles. We propose an approach that optimally interpolates between a nominal controller and the backup controller, and we derive the solution to this optimization problem in closed form. We prove that this closed-form controller is guaranteed to be safe while obeying input bounds. We demonstrate the effectiveness of the approach on a double integrator and a nonlinear fixed-wing aircraft example.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。