标题： 基于梯度的模型预测控制和控制障碍函数的安全且高效的控制器综合 显示英文标题

标题： Safe and Performant Controller Synthesis using Gradient-based Model Predictive Control and Control Barrier Functions

摘要： 确保性能和安全性对于在现实环境中运行的自主系统至关重要。 虽然安全过滤器如控制屏障函数（CBFs）通过实时修改名义控制器来强制约束，但当名义策略缺乏安全性意识时，它们可能会变得过于保守。 相反，通过动态规划求解状态约束最优控制问题（SC-OCPs）可以提供形式保证，但在高维系统中是难以处理的。 在本工作中，我们提出了一种新颖的两阶段框架，将基于梯度的模型预测控制（MPC）与基于CBF的安全过滤相结合，以协同优化安全性和性能。 在第一阶段，我们将安全约束作为成本函数中的惩罚项进行放松，从而通过基于梯度的方法实现快速优化。 这一步提高了可扩展性，并避免了与硬约束相关的可行性问题。 在第二阶段，我们使用基于CBF的二次规划（CBF-QP）对所得控制器进行修改，该方法以最小偏离参考值的方式强制执行硬性安全约束。 我们的方法生成的控制器既具有高性能，又能被证明是安全的。 我们在两个案例研究中验证了所提出的框架，展示了其在复杂、高维自主系统中合成可扩展、安全且高性能控制器的能力。 显示英文摘要

摘要： Ensuring both performance and safety is critical for autonomous systems operating in real-world environments. While safety filters such as Control Barrier Functions (CBFs) enforce constraints by modifying nominal controllers in real time, they can become overly conservative when the nominal policy lacks safety awareness. Conversely, solving State-Constrained Optimal Control Problems (SC-OCPs) via dynamic programming offers formal guarantees but is intractable in high-dimensional systems. In this work, we propose a novel two-stage framework that combines gradient-based Model Predictive Control (MPC) with CBF-based safety filtering for co-optimizing safety and performance. In the first stage, we relax safety constraints as penalties in the cost function, enabling fast optimization via gradient-based methods. This step improves scalability and avoids feasibility issues associated with hard constraints. In the second stage, we modify the resulting controller using a CBF-based Quadratic Program (CBF-QP), which enforces hard safety constraints with minimal deviation from the reference. Our approach yields controllers that are both performant and provably safe. We validate the proposed framework on two case studies, showcasing its ability to synthesize scalable, safe, and high-performance controllers for complex, high-dimensional autonomous systems.