网格缩减的自适应hp伪谱法

针对控制变量不连续的最优控制问题,本文提出一种自适应更新的忉伪谱法,这种方法在(Legendre Gauss Radau,LGR)点处取配点,能够以较小的网格规模获得较高的精度.通过计算相对误差估计,判断网格规模是增加还是缩减,若相对容许误差大于给定值,则增加网格区间数或网格配点数提高解的精度,反之则合并网格或减小网格配点数缩减网格规模提高计算效率.将hp伪谱法应用于最优控制问题,仿真验证了hp伪谱法的优越性.

Adaptive Mesh Refinement of Radau Pseudospectral Method Using Mesh Size Reduction

An adaptive mesh refinement of hp pseudospectral method is described for solving the optimal control problem when the control variable of the problem is discontinuous. The method uses orthogonal collocation at Legendre Gauss Radau points, and produces significantly smaller mesh sizes with a higher accuracy tolerance solution. The derived relative error estimate is then used to decide if the mesh size should be increased or if it should be reduced, and if the error relative error estimate is greater than the set value, then the relative error estimate is reduced by increasing the number of collocation points or increasing the number of mesh intervals, otherwise the computation time is reduced by reducing the number of collocation points or merging adjacent mesh intervals. The hp pseudospectral method is applied successfully to the examples of the optimal control problem, and the simulation experiment results show that the hp pseudospectral method has many advantages.