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.

翻译：自主系统的能力已迅速提升，但如何使其既高效又安全地执行任务仍面临挑战。性能与安全有时可能成为相互冲突的目标，这使得二者间的协同优化变得困难。一种思路是将此协同优化视为具有性能导向目标函数且以安全为约束的约束最优控制问题。然而，针对一般非线性系统求解此类约束最优控制问题仍具挑战性。在本研究中，我们采用约束最优控制的一般框架，但鉴于安全状态约束的存在，我们将其转化为等效的控制约束，从而得到一个状态与时间相关的控制约束最优控制问题。该等效最优控制问题可利用动态规划原理直接求解。我们证明了相应的值函数是某一类 Hamilton-Jacobi-Bellman 偏微分方程（HJB-PDE）的粘性解。此外，我们通过二维案例研究验证了本方法的有效性，实验表明采用本方法合成的控制器在安全性和性能方面均持续优于基线方法。