Mathematical Sciences: Computational Techniques for Control and Parameter Estimation Problems with Distributed Systems

该项目有三个主要组成部分：反馈 边界控制问题、建模和逆问题综合 生物系统的问题技术和敏感性 反问题的分析和正则化。 上 其中，将开发计算技术， 偏微分问题点边界控制 方程 应用程序包括设计和实现 大型柔性结构的控制。 在第二 反问题的数学理论将被使用， 扩展，以便结构化的数学模型 种群可以从实验中自动生成， 数据 这样一来，结构化人口的潜在规律 相互作用可以被发现或更完全地理解。 第三个主题涉及战略研究， 可以调节单一或不稳定的过程，从而 允许计算方法以某种程度的 信心 正则化参数的最佳选择是 被寻找。

This project has three major components; feedback synthesis for boundary control problems, modeling and inverse problem techniques for biological systems, and sensitivity analysis and regularization for inverse problems. In the first of these, computational techniques will be developed which will lead to point and boundary control for partial differential equations. Applications include the design and implementation of controls for large flexible structures. In the second, the mathematical theory of inverse problems will be used and extended in order that mathematical models of structured populations can be automatically generated from experimental data. In this way perhaps hidden laws of structured population interactions can be discovered or more completely understood. The third topic involves the study of strategies so that singular or unstable processes may be regulated, thereby allowing computational methods to be used with some degree of confidence. Optimal choices for regularizing parameters are to be sought.