Mathematical Sciences: Infinite Dimensional Nonlinear Programming Problems-Optimal Control Theory of Partial Differential and Functional Differential Equations

在这个项目中要做的工作分为两个相关的类别。第一类是无限维非线性规划问题，将偏微分方程、泛函微分方程和其他方程的最优控制问题建模为无限维非线性规划问题。目标包括建立最小值存在和次优元素序列收敛的必要条件。第二个主题，偏微分和泛函微分方程的最优控制理论，涉及将第一部分的结果应用于诸如最优变形问题等问题-特别是在存在障碍物的情况下。结果可能包括庞特里亚金最大原理的版本，哈密顿量的恒常性和消失性以及收敛估计。还将注意边界控制问题，其中的结果（与分布参数系统相比）是稀疏的。将应用于具体方程。

Work to be done on this project falls into two related classes. The first, infinite dimensional nonlinear programming problems, concerns the modeling of optimal control problems for partial differential equations, functional differential equations and other equations as infinite dimensional nonlinear programming problems. Goals include developing necessary conditions for the existence of minima and for the convergence of sequences of suboptimal elements. The second theme, optimal control theory of partial differential and functional differential equations concerns application of results from the first part to problems such as optimal deformation problems - especially in the presence of obstacles. The results are likely to include versions of Pontryagin's maximum principle, constancy and vanishing of the Hamiltonian and convergence estimates. Attention will also be given to boundary control questions, where results (compared to distributed parameter systems) are sparse. Application to specific equations will be made.