Multifidelity Nonsmooth Optimization and Data-Driven Model Reduction for Robust Stabilization of Large-Scale Linear Dynamical Systems

New York University, New York NY

Investigators

Abstract

Autonomous systems play an increasingly important role in engineering applications and in society as a whole, from cars to airplanes to medical devices. Truly autonomous systems will have to be able to act and make decisions under uncertainty. The key component that decides what action an autonomous system takes is the controller of the system, which guarantees that the system always remains in stable and safe states. Thus, designing controllers to stabilize systems is an important problem in a wide range of applications that include virtual or physical systems acting in an environment. The computational methodologies that will be developed in this project aim towards a reliable stabilization of large-scale systems from data alone, even when only little data and data polluted with noise are available. These algorithms have the potential to have significant impact on critical issues such as efficiency, safety, and reliability of autonomous systems. The project will promote cross-disciplinary collaborations from machine learning to control theory to numerical analysis to scientific computing and will support education and diversity by creating novel courses and outreach activities that integrate underrepresented groups in the above disciplines. Robust stabilization typically requires solving nonsmooth, nonconvex optimization problems that are computationally and mathematically challenging. Furthermore, in many situations, models of the systems of interest are unavailable. Rather, data are sampled from the systems and stabilization has to be achieved via learning from these data. This project develops and integrates new methods for nonsmooth optimization via gradient sampling and data-driven (nonintrusive) model reduction via the Loewner framework. The first contribution will be a multifidelity version of the gradient sampling algorithm for nonsmooth optimization that exploits low-cost, low-fidelity gradient approximations of a computationally expensive objective to accelerate the estimation of gradients. If successful, this multifidelity approximation has the potential to make tractable gradient sampling for large-scale optimization problems and at the same time maintain the rigorous convergence guarantees that gradient sampling is known for. The second contribution is to exploit the stability radius of robust controllers to reduce the number of data points (samples) that are required to learn reduced models for stabilizing systems. To that end, a new approach for learning reduced models from data is proposed that allows the learned models to divert from the real system dynamics by as much as can be compensated for by the robustness (stability radius) in favor of reducing the number of data points. If the project is successful, the developed methodologies will enable efficiently and rigorously stabilizing systems that are large-scale and from which few data points and/or high-noise data are available. 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.