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Extension of Unified Trigonometrization Method to Enforce Inequality Boundary Conditions in Optimal Control Problems

机译：统一三角化方法的推广在最优控制问题中强制实施不等式边界条件

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Solving optimal control problems with indirect methods is historically challenging, especially when problems contain complex features such as inequality constraints. For this reason in large part, direct methods have dominated trajectory optimization since the advent of sufficiently fast digital computers. Recently though, new methods and techniques have arisen to make indirect methods more accessible and reliable thus enabling the generation of high-quality solutions. One of these methods, the Unified Trigonometrization Method, aids solving problems with inequality path constraints on states and controls by modifying the optimal control problem. The work presented here extends the Unified Trigonometrization Method to handle inequality constraints on the initial and terminal boundaries as well. It does so by augmenting the initial and terminal cost with two-sided interior penalty functions mirroring the original method's handling of state path constraints. A variation of Zermelo's navigation problem verifies and illustrates the method, and a Space Shuttle re-entry problem demonstrates the new method's efficacy and applicability for more complex aerospace problems.
机译：解决间接方法的最佳控制问题在历史上挑战，特别是当问题包含诸如不等式约束的复杂特征时。由于这个原因在很大程度上，直接方法以足够快的数字计算机出现以来，直接方法已经主导了轨迹优化。然而，尽管如此，出现了新的方法和技术来使间接方法更容易获得和可靠，从而能够产生高质量解决方案。这些方法之一，统一三角化方法，通过修改最佳控制问题，辅助在状态和控制上对不等式路径限制解决问题。此处提出的工作扩展了统一的三角化方法，以处理初始和终端边界上的不等式约束。它通过增加双面内部惩罚功能来增加初始和终端成本，镜像原始方法的状态路径约束的处理。 Zermelo的导航问题的变体验证并说明了该方法，空间班车进入问题展示了新方法的效力和适用性，以实现更复杂的航空航天问题。

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