Discrete Approximations in Variational Problems

小行星9704912 本建议涉及无限维的数值分析 变分问题，如涉及普通的变分不等式 微分方程，微分包含和最优控制问题。 使用最近的稳定性结果，误差估计将推导出离散 状态约束最优控制问题的近似。 为 具有控制和状态约束的线性/二次问题，有效 将开发用于计算解的算法。 此外该 稳定性理论将被应用于生成先验和后验 计算解中的误差估计。 用于差分 包括，离散化将具有足够的一般性， 包含不连续右侧和状态约束的问题。 本提案中将开发的算法和理论是 适用于工业中的各种问题，例如与 机器人的最佳性能，航空航天飞行控制， 具有所需性能的薄膜，或化学的最佳工程， 流程.当这些问题中的任何一个在计算机上得到解决时， 将连续过程分解为微小的时间步。 这项建议 研究了当这个连续过程离散化时所引起的误差 用这种方式。

9704912 Hager This proposal concerns the numerical analysis of infinite dimensional variational problems such as variational inequalities involving ordinary differential equations, differential inclusions, and optimal control problems. Using recent stability results, errors estimates will be derived for discrete approximations of state constrained optimal control problems. For linear/quadratic problems with control and state constraints, efficient algorithms will be developed for computing a solution. In addition, the stability theory will be applied to generate both a priori and a posteriori estimates for the errors in the computed solutions. For differential inclusions, discretizations will be developed with sufficient generality to encompass problems with discontinuous right sides and state constraints. The algorithms and theory that will be developed in this proposal are applicable to a variety of problems in industry such as those associated with the optimal performance of robots, flight control in aerospace, the design of thin films with desired properties, or the optimal engineering of chemical processes. When any of these problems is solved on a computer, the continuous process is decomposed into tiny time steps. This proposal studies the errors that are caused when this continuous process is discretized in this way.