Mathematical Sciences: Methods of Non-Smooth Analysis In Optimal Control

数学科学：最优控制中的非光滑分析方法

• 批准号: 8701768
• 负责人: Domokos Vermes
• 金额: $ 3.19万
• 依托单位: University of Washington
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-06-15 至 1990-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8701768&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Methods; Non; Smooth

The objective of this research is to use the notions and methods of non-smooth analysis to establish a new type of connection between optimal stochastic control problems and the Hamilton- Jacobi-Bellman equation irrespective of the possible degeneracy properties of the underlying processes. This would provide a new insight into the interrelation between variational problems and certain nonlinear partial differential equations as well as a unified approach to both deterministic and stochastic optimal control theory. The core of the research is the investigation of the regularity of properties of the optimal value function in terms of its subdifferentials, Clarke derivatives and the finding of a class of non-smooth functions in which the Hamilton-Jacobi- Bellman equation is uniquely solvable. Accumulation of computational and modeling experience on application problems are also parts of the project.

本研究的目的是运用 建立一种新型的非光滑分析连接 最优随机控制问题和汉密尔顿- 不考虑可能简并的Jacobi-Bellman方程 底层进程的属性。 这将提供一个新的 深入了解变分问题之间的相互关系， 某些非线性偏微分方程以及 确定性和随机性最优解的统一方法 控制理论 本研究的核心是调查 最优值函数性质的正则性 项的次微分，Clarke导数和发现 一类非光滑函数，其中Hamilton-Jacobi- Bellman方程是唯一可解的。 积累 在应用问题上的计算和建模经验， 也是项目的一部分。