Mathematical Sciences: Exchange Program with St. Petersburg State University; Harmonic Analysis and Control of Linear Partial Differential Eq'ns

该项目将支持弗吉尼亚理工学院和州立大学、马里兰大学、巴尔的摩县大学和俄罗斯圣彼得堡州立大学的联合交流计划。本次交流计划的目的是让参与者探索非调和傅立叶级数的理论发展与分布参数系统的控制、估计和识别理论的潜在应用之间的深层联系。事实上，非调和傅立叶级数理论的最新进展发生在俄罗斯和前苏联，而应用在美国取得了巨大的进步，这使得这个交流项目特别及时。该计划将安排五次单独访问，其中两次由美国代表团访问俄罗斯，三次由俄罗斯代表团访问美国。在分布参数系统的控制、估计和识别中使用非调和傅立叶级数方法，至少可以追溯到1963年，现在越来越重要，因为新复杂的先进材料生产和加工需要复杂的非侵入性状态估计技术。非调和傅立叶级数技术允许从外部收集的温度、浓度等数据中产生过程的内部状态估计，而不需要侵入性的内部探测，可能会干扰过程。

9501036 Russell This project will support a joint exchange program involving Virginia Polytechnic Institute and State University, University of Maryland, Baltimore County and St. Petersburg State University in Russia. The purpose of this exchange program is to allow the participants to explore deep interconnections between theoretical developments in nonharmonic Fourier series and potential applications in the control, estimation and identification theory of distributed parameter systems. The fact that most recent advances in the theory of nonharmonic Fourier series have taken place in Russia and the former Soviet Union, while applications have enjoyed dramatic advances in the United States, makes this exchange program particularly timely. The program envisages five separate visits, two on the part of United States participants to Russia and three involving Russian visitors to the United States. The use of nonharmonic Fourier series methods in control, estimation and identification of distributed parameter systems, which dates back at least to 1963, is now of increasing importance because of sophisticated non- invasive state estimation techniques required for newly sophisticated advanced materials production and processing. Nonharmonic Fourier series techniques allow estimates of the interior state of a process to be generated from externally collected data on temperatures, concentrations, etc., without the need for invasive internal probing potentially interfering with the process.