Robust Optimization of Nonlinear Dynamical Systems

University Of Connecticut, Storrs CT

Investigators

Abstract

The increasing emphasis on robust system designs for manufacturing, defense, and energy applications, among others, is motivating design engineers to use high-fidelity models that account for complex nonlinear behavior and uncertainty in parameter values. This research project will develop novel methods and easy-to-use software for engineers to account for uncertainty at the design stage. These products will dramatically improve the design capabilities in nearly every industry, resulting in safer, more reliable, more robust, and more cost-effective designs of engineered systems. As part of this research project a graduate student will be trained in cutting edge research. Also, a new module on the robust design of dynamical systems will be developed to introduce formal dynamical systems under uncertainty to systems engineers from industry through a graduate online course on Uncertainty Analysis, Robust Design, and Optimization. The objective of this research project is to solve the robust design problem for systems modeled as initial value problems which is formulated as a bi-level, max/min, and/or semi-infinite optimization problem. Solving this problem requires establishing new theoretical mathematics, numerical analysis, and high-speed software implementations for combining dynamic simulation and deterministic global optimization. The development of McCormick-based relaxations of implicit functions is proposed for use within deterministic global optimization frameworks for global bounding information. These developments will be implemented in a software library written in the Julia programming language for high speed and accessibility. Improved systems design results in greater safety and security which benefits society by reducing the impacts of catastrophic operational failures or eliminating them altogether. Improved designs also result in reduced production costs and reduced environmental impact through efficiency improvements which directly benefit society by reducing costs of products (e.g., commodities, energy, consumer goods, transportation, etc.). This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.