A general-purpose C++ software program called CGPOPS is described for solving multiple-phase optimal control problems using adaptive direct orthogonal collocation methods. The software employs a Legendre-Gauss-Radau direct orthogonal collocation method to transcribe the continuous optimal control problem into a large sparse nonlinear programming problem (NLP). A class of hp mesh refinement methods are implemented that determine the number of mesh intervals and the degree of the approximating polynomial within each mesh interval to achieve a specified accuracy tolerance. The software is interfaced with the open source Newton NLP solver IPOPT. All derivatives required by the NLP solver are computed via central finite differencing, bicomplex-step derivative approximations, hyper-dual derivative approximations, or automatic differentiation. The key components of the software are described in detail, and the utility of the software is demonstrated on five optimal control problems of varying complexity. The software described in this article provides researchers a transitional platform to solve a wide variety of complex constrained optimal control problems.

中文翻译：

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CGPOPS

描述了一种称为 CGPOPS 的通用 C++ 软件程序，用于使用自适应直接正交配置方法解决多相最优控制问题。该软件采用Legendre-Gauss-Radau直接正交搭配方法将连续最优控制问题转化为大型稀疏非线性规划问题（NLP）。一类生命值实施网格细化方法，确定网格间隔的数量和每个网格间隔内的近似多项式的次数，以达到指定的精度容差。该软件与开源 Newton NLP 求解器 IPOPT 连接。NLP 求解器所需的所有导数都是通过中心有限差分、双复步导数逼近、超对偶导数逼近或自动微分计算的。详细描述了软件的关键组件，并在五个复杂度不同的最优控制问题上展示了该软件的实用性。本文介绍的软件为研究人员提供了一个过渡平台，可以解决各种复杂的约束最优控制问题。