This study investigates the use of trigonometric functions to resolve two major issues encountered when solving practical optimal control problems (OCPs) that are characterized by nonlinear controls. First, OCPs with constraints on nonlinear controls require the solution to a multipoint boundary value problem, which poses additional computational difficulties. Second, in certain unconstrained OCPs with nonlinear controls, the extremum found from the necessary conditions can be opposite than expected (e.g., a maximum instead of a minimum) due to the absence of control options. The aforementioned issues and their effective resolution by using trigonometric functions are explained through two examples including a second‐order system problem and an aerocapture problem of a slender entry vehicle in the Martian atmosphere.

中文翻译：

---

使用三角函数解决非线性控制的复杂最优控制问题

这项研究调查了三角函数的使用，以解决解决以非线性控制为特征的实际最优控制问题（OCP）时遇到的两个主要问题。首先，受非线性控制约束的OCP需要解决多点边界值问题，这带来了额外的计算困难。其次，在某些具有非线性控制的无约束OCP中，由于缺少控制选项，从必要条件中找到的极值可能与预期相反（例如，最大值而不是最小值）。通过两个示例解释了上述问题及其使用三角函数的有效解决方案，其中包括二阶系统问题和细长型进入火星车在火星大气层中的航空捕获问题。