Computational Methods for Identification, Optimization and Control of PDE Systems

摘要

The research focused on the construction of high fidelity numerical methods and the development of a rigorous mathematical framework for attacking complex optimization and control problems with partial differential equations (PDEs) as constraints. The research is motivated by applications to two distinct but related application areas: (1) Optimal design and control of ultra- light large space structures which will serve as the platforms for many future space applications such as space-based radar; (2) Optimal design and control of flexible air vehicles and feedback control of fundamental fluid flows. We generated new numerical methods specifically for parameter estimation, shape optimization, optimal control and feedback control of PDE systems of the type that govern ultra-light inflatable space structures, aero-dynamic design and fluid flows. We developed a rigorous mathematical framework to analyze convergence of the resulting control, design and optimization algorithms, obtain error estimates and rates of convergence.