AF: Small: Data-Driven Model Reduction for Optimal Control of Large-Scale Systems

William Marsh Rice University, Houston TX

Investigators

Abstract

Dynamical systems are a principal tool in the modeling, prediction, and control of physical phenomena ranging from heat dissipation in complex microelectronic devices, to vibration suppression in large wind turbines, to flow simulation. Optimal control of dynamical systems plays an important role in the many science and engineering applications where one wants to generate inputs to improve the performance of a system. However, ever-increasing need to include more detail at the modeling stage inevitably leads to larger-scale, more complex dynamical systems. Many of these large-scale systems are obtained from spatial discretizations of time-dependent coupled systems of partial differential equations. The simulation of such complex dynamical systems creates huge demands on computational resources and such high fidelity simulations may become unmanageable when the system needs to be queried at many different inputs. This project develops and applies a new class of model reduction methods for the efficient simulation and optimal control of dynamical systems. The model reduction approaches developed in this project approximate large, complex models of time-dependent processes using smaller, computationally efficient models that are nonetheless capable of representing accurately the outputs of the original process under a variety of operating conditions. Thus the new model reduction methods allow simulation and control of systems that would otherwise not be practical with high fidelity computational models. The new model reduction methods developed in this project are data-driven. Unlike existing methods, in many cases, the new methods allow the generation of efficient reduced order computational models directly from (experimental) data and do not require access to high fidelity computational simulations. Overall, this new approach offers several advancements. First, it generates a reduced order model of the original nonlinear dynamical system that is valid for all inputs. Second, the new approach is data-driven and avoids the use of projections. This means less detailed access to the components of the original system are needed, which makes the new method particularly attractive when details of system simulation is inaccessible. This project will develop mathematical algorithms for the creation of such data-driven reduced order models and provide theoretical analyses of their performance. In addition, this project integrates the new model reduction approach into the solution of optimal control problems. For this integration, crucial additional input-output relations will be identified and the reduced order model generation will be augmented to ensure that these additional input-output relations are well approximated. This new approach will be applied to simulation and control of important biological phenomena and of fluid flows. 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.