标题： 无优化快速最优控制：突变-滑行特性、单调性及在快速电池充电中的应用 显示英文标题

标题： Optimization-Free Fast Optimal Control: Bang-Ride Property, Monotonicity, and Applications to Fast Battery Charging

摘要： 单输入快速最优控制问题，旨在尽可能快地实现最优目标，在各种现实应用中都会出现。 在快速电池充电的情况下，当使用详细的电池模型时，相关的最优控制问题会变得计算上具有挑战性。 一种最近的无启发式优化算法可以显著降低计算成本，并提供一个近似解，与实践中许多启发式输入配置一致。 这些启发式解有几个特殊性质：它们遵循一种“bang-ride”模式，始终激活一个约束并应用最大可行输入。 这项工作研究了上述性质何时出现在最优输入中，以及最终启发式输入配置何时满足必要最优性条件。 通过利用庞特里亚金最大原理（PMP），我们证明在约束切换和系统局部可控性的常规条件下，最优控制是“bang-ride”形式。 此外，在系统、目标函数和约束的限制灵敏度单调的情况下，特定类型的“bang-ride”行为，即应用最大可行输入，会出现。 这些结果为一类充电启发式方法和快速无优化算法提供了理论依据。 显示英文摘要

摘要： Single-input fast optimal control problems, which aim to achieve the optimal objective as fast as possible, occur in various real-world applications. In the case of fast battery charging, the associated optimal control problem becomes computationally challenging when detailed battery models are used. A recent heuristic optimization-free algorithm can significantly reduce the computational cost and provide an approximate solution, consistent with many heuristic input profiles in practice. These heuristic solutions have several special properties: They follow a bang-ride pattern that always activates a constraint and applies the maximum feasible input. This work investigates when the above properties arise in the optimal input, and ultimately, when the heuristic input profiles satisfy necessary optimality conditions. By exploiting Pontryagin's maximum principle (PMP), we show that the optimal control is bang-ride under regularity conditions on constraint switching and local controllability of the system. Moreover, the special type of bang-ride behavior, i.e., applying the maximum feasible input, arises under the monotonicity of the system, objective function, and restricted sensitivity of the constraints. These results provide a theoretical justification for a class of charging heuristics and the fast optimization-free algorithm.