基于李雅普诺夫的非线性安全控制框架，提升安全区域和稳定性。
Barrier-Riccati Synthesis for Nonlinear Safe Control with Expanded Region of Attraction
- 用辅助状态将安全约束嵌入动态，实现安全作为控制目标。
- 通过SDRE求解点态黎卡提方程，扩大吸引域并保证渐近安全稳定。
- 适用于无人机等高危场景，对边界附近扰动鲁棒性强。
我们提出一种基于黎卡提方程的非线性安全控制框架，融合障碍状态（BaS）方法与状态依赖黎卡提方程（SDRE）技术。该框架通过辅助状态将安全约束嵌入系统动力学，使安全成为可优化的控制目标。为克服线性BaS控制器吸引域有限的问题，我们扩展至非线性系统，对增强后的障碍动力学应用SDRE合成，并推导出矩阵不等式条件，以保证大范围吸引域的前向不变性及渐近安全稳定。控制器通过逐点求解黎卡提方程在线计算。在不稳定受约束系统和杂乱环境下的四旋翼导航任务中验证了该方法，表现出更优的约束处理能力、可扩展性及靠近安全边界的鲁棒性。该框架为安全关键环境中非线性安全反馈控制提供了理论严谨且计算可行的解决方案。
原文摘要 · Abstract (English)
We present a Riccati-based framework for safety-critical nonlinear control that integrates the barrier states (BaS) methodology with the State-Dependent Riccati Equation (SDRE) approach. The BaS formulation embeds safety constraints into the system dynamics via auxiliary states, enabling safety to be treated as a control objective. To overcome the limited region of attraction in linear BaS controllers, we extend the framework to nonlinear systems using SDRE synthesis applied to the barrier-augmented dynamics and derive a matrix inequality condition that certifies forward invariance of a large region of attraction and guarantees asymptotic safe stabilization. The resulting controller is computed online via pointwise Riccati solutions. We validate the method on an unstable constrained system and cluttered quadrotor navigation tasks, demonstrating improved constraint handling, scalability, and robustness near safety boundaries. This framework offers a principled and computationally tractable solution for synthesizing nonlinear safe feedback in safety-critical environments.
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