将安全与性能协同优化转化为可控约束问题，提升自主系统安全性与效率。
Cooptimizing Safety and Performance with a Control-Constrained Formulation
- 将安全约束转为控制约束，用动态规划求解复杂非线性系统。
- 理论证明值函数是HJB-PDE的黏性解，确保解的数学正确性。
- 二维实验表明方法在安全性和性能上均优于基线模型。
自主系统能力迅速提升，但如何同时实现高效与安全仍具挑战。性能与安全常存在冲突，现有方法常将其建模为以性能为导向的目标函数、安全为约束的约束最优控制问题。然而，对一般非线性系统求解此类问题仍困难重重。本文采用约束最优控制通用框架，针对安全状态约束，将其等价转换为状态和时间依赖的控制约束，形成新的控制约束最优控制问题。该问题可直接使用动态规划原理求解。我们证明对应的值函数是特定哈密顿-雅可比-贝尔曼偏微分方程（HJB-PDE）的黏性解。通过二维案例研究验证了方法有效性，实验结果表明，基于该方法合成的控制器在安全性和性能上均持续优于基线方法。
原文摘要 · Abstract (English)
Autonomous systems have witnessed a rapid increase in their capabilities, but it remains a challenge for them to perform tasks both effectively and safely. The fact that performance and safety can sometimes be competing objectives renders the cooptimization between them difficult. One school of thought is to treat this cooptimization as a constrained optimal control problem with a performance-oriented objective function and safety as a constraint. However, solving this constrained optimal control problem for general nonlinear systems remains challenging. In this work, we use the general framework of constrained optimal control, but given the safety state constraint, we convert it into an equivalent control constraint, resulting in a state and time-dependent control-constrained optimal control problem. This equivalent optimal control problem can readily be solved using the dynamic programming principle. We show the corresponding value function is a viscosity solution of a certain Hamilton-Jacobi-Bellman Partial Differential Equation (HJB-PDE). Furthermore, we demonstrate the effectiveness of our method with a two-dimensional case study, and the experiment shows that the controller synthesized using our method consistently outperforms the baselines, both in safety and performance.
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