标题： 直接射击法用于数值最优控制：一种修改的转录方法 显示英文标题

标题： Direct Shooting Method for Numerical Optimal Control: A Modified Transcription Approach

摘要： 直接射击是一种高效求解数值最优控制的方法。 它利用龙格-库塔格式对连续时间最优控制问题进行离散化，使问题能够通过非线性规划求解器求解。 然而，当使用扩展状态处理{高阶}系统时，传统的直接射击方法会引发矛盾的动力学问题。 本文通过考虑{高阶}系统的直接射击方法来填补研究空白。 我们推导了修正欧拉法和龙格-库塔-4方法，以直接转录系统动力学约束。 此外，我们提供了所提出方法的全局误差上界。 一组基准最优控制问题表明，我们的方法比现有方法提供更精确的解决方案。 显示英文摘要

摘要： Direct shooting is an efficient method to solve numerical optimal control. It utilizes the Runge-Kutta scheme to discretize a continuous-time optimal control problem making the problem solvable by nonlinear programming solvers. However, conventional direct shooting raises a contradictory dynamics issue when using an augmented state to handle {high-order} systems. This paper fills the research gap by considering the direct shooting method for {high-order} systems. We derive the modified Euler and Runge-Kutta-4 methods to transcribe the system dynamics constraint directly. Additionally, we provide the global error upper bounds of our proposed methods. A set of benchmark optimal control problems shows that our methods provide more accurate solutions than existing approaches.