Mathematical Sciences: Lipschitz Stability and Its Application to Numerical Analysis in Optimal Control

数学科学：Lipschitz 稳定性及其在最优控制数值分析中的应用

• 批准号: 9404431
• 负责人: William Hager
• 金额: $ 9.6万
• 依托单位: University of Florida
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-06-01 至 1998-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9404431&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Lipschitz; Stability; Its

9404431 Hager/Dontchev This research will pursue the applications of recent implicit function-type results for set-valued maps in an infinite dimensional setting to numerical algorithms for optimal control problems and the Lipschitz properties of their solutions. This work considers control problems with state and control constraints for which there are many open questions. Log-barrier approaches to control constraints will be investigated, and error estimates for discretizations will be derived. This research will develop and analyze numerical algorithms for solving optimal control problems with control and state constraints. In particular, the possible Lipschitz properties of optimal solutions will be investigated. Knowledge of the Lipschitz continuity of the solution is important, for instance, in the study of the convergence behavior of various numerical approximations for the solution. Anticipated applications of the research include problems in computer aided geometric design, and optimal motion planning of a flexible structure (such as a robot or a crane) in the presence of obstacles.

9404431 Hager/Dontchev 这项研究将追求无限维设置中集值映射的最新隐函数类型结果在最优控制问题的数值算法及其解决方案的 Lipschitz 属性中的应用。 这项工作考虑了具有状态和控制约束的控制问题，其中存在许多悬而未决的问题。将研究控制约束的对数屏障方法，并导出离散化的误差估计。 本研究将开发和分析用于解决具有控制和状态约束的最优控制问题的数值算法。特别是，将研究最优解的可能的利普希茨性质。了解解的 Lipschitz 连续性非常重要，例如，在研究解的各种数值近似的收敛行为时。该研究的预期应用包括计算机辅助几何设计中的问题，以及存在障碍物时柔性结构（例如机器人或起重机）的最佳运动规划。