Modified Radau Collocation Method for Solving Optimal Control Problems with Nonsmooth Solutions Part II: Costate Estimation and the Transformed Adjoint System
Modified Radau Collocation Method for Solving Optimal Control Problems with Nonsmooth Solutions Part II: Costate Estimation and the Transformed Adjoint System
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DOI：
10.1109/cdc.2018.8619426
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发表时间：
2018-12
期刊：
影响因子：
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通讯作者：
Joseph D. Eide;W. Hager;Anil V. Rao
中科院分区：
文献类型：
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作者：
Joseph D. Eide;W. Hager;Anil V. Rao
提出了一种改进的legende - gauss - radau配置法，用于求解包含非光滑最优控制的最优控制问题。该方法包含一个附加变量，用于定义不平滑的位置。此外，在网格间隔的末端添加了搭配约束，该网格间隔定义了每个微分方程的解中非光滑的位置，微分方程是控制的函数，并且在同一网格间隔的端点处有控制约束。然后导出了改进的legende - gaas - radau配置法的变换伴随系统，以及非线性规划问题的拉格朗日乘子与最优控制问题的离散近似之间的关系。最后，通过实例表明，该方法能较准确地逼近状态。
A modified Legendre-Gauss-Radau collocation method is developed for solving optimal control problems whose solutions contain a nonsmooth optimal control. The method includes an additional variable that defines the location of nonsmoothness. In addition, collocation constraints are added at the end of a mesh interval that defines the location of nonsmoothness in the solution on each differential equation that is a function of control along with a control constraint at the endpoint of this same mesh interval. The transformed adjoint system for the modified Legendre-Gauss-Radau collocation method along with a relationship between the Lagrange multipliers of the nonlinear programming problem and a discrete approximation of the costate of the optimal control problem is then derived. Finally, it is shown via example that the new method provides an accurate approximation of the costate.