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

该项目包括三个主要部分：边界控制问题的反馈综合，生物系统的建模和反问题技术，以及反问题的灵敏度分析和正则化。首先，我们将发展一些计算技术来解决偏微分方程点和边界的控制问题。应用包括设计和实施大型柔性结构的控制。第二，反问题的数学理论将被使用和扩展，以便从实验数据自动生成结构化总体的数学模型。通过这种方式，或许可以发现或更完整地理解结构化种群相互作用的隐藏规律。第三个主题涉及对战略的研究，以便可以对单一或不稳定的过程进行监管，从而使计算方法能够在一定程度上有把握地使用。寻求正则化参数的最佳选择。

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.