Collaborative Research: A Constrained Optimal Control Approach to Nonparametric Estimation with Applications to Biological, Biomedical and Engineering Systems

该奖项的研究目标是开发一种控制理论框架和有效的数值格式，用于形状和动力学约束函数的非参数估计，并应用于新兴领域，如系统生物学。该项目将集中于三个重要且相互关联的部分：(I)受约束函数的光滑样条估计；(Ii)受约束函数的惩罚多项式样条估计器的计算和分析；以及(Iii)在遗传调控网络、可靠性工程中的退化分析和生物医学研究中的联合药物治疗中的应用。基本的理论基础是基于约束最优控制、互补理论和渐近统计。所得到的估计算法将在各种受约束的生物、生物医学和工程系统上实现，约束在工程和科学中普遍存在。这项研究中开发的有效评估方法将使人们更好地了解复杂的生物系统，并对产品的寿命和联合药物对患者的影响提供准确的预测。拟议的研究超越了传统的控制技术领域，在统计学、系统生物学、可靠性工程和生物医学实践中有许多新的应用。该项目的研究成果将通过PIS与工程师和流行病学家的密切合作进行传播。该项目还打算将研究与马里兰州大学、巴尔的摩县大学和普渡大学的教育和外联活动结合起来。例如，开发新课程和招收学生以获得实践研究经验。将支持本科暑期研究和K-12培训，特别注重少数群体和妇女参与者。

The research objective of this award is to develop a control theoretic framework and efficient numerical schemes for nonparametric estimation of shape and dynamics constrained functions, with applications to emerging fields such as systems biology. The project will focus on three important and interrelated components: (i) smoothing spline estimation of functions subject to constraints; (ii) computation and analysis of penalized polynomial spline estimators for constrained functions; and (iii) applications to genetic regulatory networks, degradation analysis in reliability engineering, and joint-drug treatment in biomedical research. The underlying theoretical foundation is based on constrained optimal control, complementarity theory, and asymptotic statistics. The obtained estimation algorithms will be implemented on various biological, biomedical and engineering systems subject to constraints.Constraints are pervasive in engineering and science. Efficient estimation methods to be developed in this research will yield better understanding of complex biological systems, and provide accurate predication of products' lifetime and joint-drug effects on patients. The proposed research goes beyond traditional areas of control technology with many novel applications in statistics, systems biology, reliability engineering, and biomedical practice. The research findings of this project will be disseminated through PIs' close collaboration with engineers and an epidemiologist. This project also intends to integrate research with education and outreach activities at University of Maryland Baltimore County and Purdue University. Examples include developing new curricula and recruiting students to gain hands-on research experience. Undergraduate summer research and K-12 training will be supported with particular focus on minority and women participants.