论文标题
快速准确的方法来计算非平滑解决方案以限制控制问题
Fast and accurate method for computing non-smooth solutions to constrained control problems
论文作者
论文摘要
在时间限制网格中引入灵活性可以改善收敛性和计算时间，而在数值上求解微分方程时，尤其是当解决方案是不连续的时，正如在具有约束的控制问题中所发现的那样。最先进的方法使用固定的网格方案，在存在非平滑溶液的情况下无法实现超线性收敛。在本文中，我们建议在集成的残差方法中使用灵活的网格。网格节点的位置是作为决策变量引入的，并将约束添加到网格间隔大小的上限和下限。我们将我们的方法与现实卫星重新定向示例上的均匀固定网格进行了比较。该示例表明，灵活的网格使求解器能够自动定位解决方案中的不连续性，具有超线收敛性和更快的求解时间，同时达到与固定网格相同的准确性。
Introducing flexibility in the time-discretisation mesh can improve convergence and computational time when solving differential equations numerically, particularly when the solutions are discontinuous, as commonly found in control problems with constraints. State-of-the-art methods use fixed mesh schemes, which cannot achieve superlinear convergence in the presence of non-smooth solutions. In this paper, we propose using a flexible mesh in an integrated residual method. The locations of the mesh nodes are introduced as decision variables, and constraints are added to set upper and lower bounds on the size of the mesh intervals. We compare our approach to a uniform fixed mesh on a real-world satellite reorientation example. This example demonstrates that the flexible mesh enables the solver to automatically locate the discontinuities in the solution, has superlinear convergence and faster solve times, while achieving the same accuracy as a fixed mesh.
