• 主题
高级搜索  >
历史搜索 清空历史
首页> 外文会议>AIAA Guidance, Navigation and Control Conference Pt.1, Aug 1-3, 1994, Scottsdale, AZ >STABILIZATION OF NUMERICAL SOLUTIONS OF BOUNDARY VALUE PROBLEMS EXPLOITING INVARIANTS
【24h】

STABILIZATION OF NUMERICAL SOLUTIONS OF BOUNDARY VALUE PROBLEMS EXPLOITING INVARIANTS

机译：探索不变变量的边值问题的数值解的稳定化

获取原文
获取原文并翻译 | 示例
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

Solving boundary value problems (BVPs) numerically is an important task when dealing with problems of optimal control. In this paper the numerical solution of BVPs for differential algebraic equations (DAEs) is discussed. The method of choice is multiple shooting. Optimal control problems are higher index DAEs in the case of singular controls or state constraints. The common procedure of solving higher index DAEs is to reduce the index by differentiating the algebraic equations until index 1 DAEs or ordinary differential equations (ODEs) are obtained which can be treated directly. Unfortunately, the numerical solution of the index reduced problems often suffers from instabilities introducing a drift from the original algebraic conditions. We inter-prete the higher index constraints as invariants of the ODE and exploit these invariants in order to improve accuracy, stability and efficiency by a new projection technique. Obviously, conservation properties e.g. for energy or momentum can be used in this sense, but the symplectic structure of Pontryagin's Maximum principle allows for deriving further invariants. Solving the shooting equations by Newton's method requires the computation of sensitivity matrices. This is performed by solving the initial value problems for the variational ODEs together with their invariants or by differentiation of the discretization scheme. The techniques are demonstrated on the example of a flight path optimization problem.
机译：数值求解边界值问题（BVP）是处理最佳控制问题时的重要任务。本文讨论了微分代数方程（DAE）的BVP的数值解。选择的方法是多重拍摄。最佳控制问题是在单一控制或状态约束的情况下具有较高索引的DAE。解决高指数DAE的常见过程是通过微分代数方程来减少指数，直到获得可以直接处理的指数1 DAE或常微分方程（ODE）。不幸的是，指数减小问题的数值解常常遭受不稳定性的影响，该不稳定性引入了与原始代数条件的偏差。我们将较高的索引约束解释为ODE的不变量，并利用这些不变量来通过新的投影技术提高准确性，稳定性和效率。显然，保护特性例如在这种意义上可以使用能量或动量，但庞特里亚金极值原理的辛结构允许推导进一步的不变性。用牛顿法求解射击方程需要计算灵敏度矩阵。这是通过求解变分ODE及其不变量的初值问题或通过离散化方案的区分来完成的。以飞行路径优化问题为例演示了这些技术。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号