AdaptiveMesh RefinementMethod for Optimal Control Using Nonsmoothness Detection andMesh Size Reduction
AdaptiveMesh RefinementMethod for Optimal Control Using Nonsmoothness Detection andMesh Size Reduction
复制标题
使用非光滑度检测和网格尺寸减小进行最优控制的自适应网格细化方法
DOI：
10.1016/j.franklin.2015.05.028
复制
发表时间：
2015
期刊：
影响因子：
--
通讯作者：
Liu, F.
中科院分区：
文献类型：
--
作者：
Liu, F.
提出了一种求解最优控制问题的自适应网格加密方法。该方法在Legendre-Gauss-Radau点处采用正交配置，并在加密过程中调整网格尺寸和逼近多项式的阶数。一个先前推导的收敛速度是用来指导细化过程。该方法括号的不连续性，并通过检查状态的高阶导数的大幅增加，提高了解决方案的精度。在间断之间的区域中，其中解是光滑的，通过增加近似多项式的次数来减少近似中的误差。在满足误差容限的网格间隔上，可以通过合并相邻的网格间隔或降低近似多项式的次数来降低网格密度。最后，该方法证明了两个例子，从公开文献和它的性能进行比较，对以前开发的自适应方法。
An adaptive mesh refinement method for solving optimal control problems is developed. The method employs orthogonal collocation at Legendre–Gauss–Radau points, and adjusts both the mesh size and the degree of the approximating polynomials in the refinement process. A previously derived convergence rate is used to guide the refinement process. The method brackets discontinuities and improves solution accuracy by checking for large increases in higher-order derivatives of the state. In regions between discontinuities, where the solution is smooth, the error in the approximation is reduced by increasing the degree of the approximating polynomial. On mesh intervals where the error tolerance has been met, mesh density may be reduced either by merging adjacent mesh intervals or lowering the degree of the approximating polynomial. Finally, the method is demonstrated on two examples from the open literature and its performance is compared against a previously developed adaptive method.