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

Purdue University, West Lafayette IN

Investigators

Abstract

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.