Model Order Reduction using Similarity Notions

Abstract

Model order reduction is a classical problem that aims to determine a low-order approximation of high-order models. Many methods are available for linear systems, each with its own advantages and limitations. We argue that using recent developments in approximate bisimulation of continuous systems yields a model order reduction framework that has some unique properties. For one, the resulting reduced order model (ROM) is robust to any disturbance that acts on the full order model (FOM) — in the sense that the output of the ROM remains a good approximation of that of the FOM, even in the presence of arbitrary disturbances. Further, the ROMs display compositionality properties in the sense that ROMs of interconnected subsystems when composed yield an ROM of the system itself. In particular, this means we can provide a provable bound on the output of the FOM when a controller designed for the ROM is used with the FOM. The proposed framework is compatible with existing approaches such as balanced truncation and moment matching. This is joint work with Shivam Bajaj, Prateek Jaiswal, and Carolyn Beck.

Biography

Vijay Gupta is the Elmore Professor of Electrical and Computer Engineering and the Associate Head for Graduate and Professional Programs in ECE at the Purdue University, having joined the faculty in May 2022. He received his B. Tech degree at Indian Institute of Technology, Delhi, and his M.S. and Ph.D. at California Institute of Technology, all in Electrical Engineering. He previously served as a research associate at the University of Maryland, College Park, a consultant at the United Technologies Research Center, and as a faculty member at University of Notre Dame. He is a Fellow of IEEE and IFAC. He received the 2018 Antonio Ruberti Young Research Award from the IEEE Control Systems Society, the 2013 Donald P. Eckman Award from the American Automatic Control Council, and an 2009 National Science Foundation (NSF) CAREER Award. He is a distinguished lecturer for IEEE Control Systems Society, 2023-25. His research and teaching interests are at the interface of learning, game theory, and distributed systems.