标题： 航空航天应用中求解复杂非线性决策问题的MINLP和MPVC公式比较研究 显示英文标题

标题： A Comparative Study of MINLP and MPVC Formulations for Solving Complex Nonlinear Decision-Making Problems in Aerospace Applications

摘要： 对于动态系统的高层次决策通常涉及性能和安全规格，这些规格会根据与系统状态和命令相关的条件而激活或停用。 此类决策问题可以自然地表述为优化问题，其中这些条件性激活由离散变量调节。 然而，在强大的计算平台上求解这些问题也可能具有挑战性，尤其是当动力学是非线性的时候。 在这项工作中，我们考虑了非线性系统的决策问题，其中某些约束以及成本函数中的可能项会根据系统状态和命令激活或停用。 我们展示了这些问题可以被表述为混合整数非线性规划（MINLP）或者带有消失约束的数学规划（MPVC），其中前者涉及离散决策变量，而后者依赖于受结构化非凸约束的连续变量。 我们讨论了两种表述方法可用的不同求解方法，并在各种航空航天应用中的最优轨迹规划问题上进行了演示。 最后，我们通过一个专注于带偏移可行区域的推进下降制导的聚焦案例研究，比较了MINLP和MPVC方法的优点和缺点。 显示英文摘要

摘要： High-level decision-making for dynamical systems often involves performance and safety specifications that are activated or deactivated depending on conditions related to the system state and commands. Such decision-making problems can be naturally formulated as optimization problems where these conditional activations are regulated by discrete variables. However, solving these problems can be challenging numerically, even on powerful computing platforms, especially when the dynamics are nonlinear. In this work, we consider decision-making for nonlinear systems where certain constraints, as well as possible terms in the cost function, are activated or deactivated depending on the system state and commands. We show that these problems can be formulated either as mixed-integer nonlinear programs (MINLPs) or as mathematical programs with vanishing constraints (MPVCs), where the former formulation involves discrete decision variables, whereas the latter relies on continuous variables subject to structured nonconvex constraints. We discuss the different solution methods available for both formulations and demonstrate them on optimal trajectory planning problems in various aerospace applications. Finally, we compare the strengths and weaknesses of the MINLP and MPVC approaches through a focused case study on powered descent guidance with divert-feasible regions.