When
Thursday, October 1, 2026 at 4:00 p.m.
Boris Kramer
Associate Professor
Department of Mechanical and Aerospace Engineering
University of California, San Diego
AME Lecture Hall, Room S212 | Zoom link
"Balanced Truncation Model Reduction and Control of High-Dimensional Nonlinear Systems"
Abstract: Optimal control of high-dimensional nonlinear systems is challenging from a computational perspective, as it requires solving nonlinear optimality systems in high dimensions. Nonlinear model reduction for control systems is one avenue to this problem, yet the model reduction problem in turn requires solving high-dimensional control problems in the first place to find the proper projections and manifolds where reduced trajectories evolve. Thus, the nonlinear control and model reduction problem are intricately related. In this talk, we build on the theoretically rigorous framework of nonlinear balanced truncation model reduction, a system-theoretic method that is built on the notion of controllability and observability of a nonlinear system. The framework requires solving well-behaved high-dimensional Hamilton-Jacobi-Bellman partial differential equations, which we do so with Taylor-series-based techniques to produce scalable algorithms for systems with 1,000s of state variables. We then describe ways to use these solutions to control nonlinear systems, even going to 100,000s of dimension through some additional approximations, as well as how to derive nonlinear balanced truncation ROMs. We illustrate the methods on a variety of problems in aerospace, mechanical engineering and fluids.
Bio: Boris Kramer is an associate professor in mechanical and aerospace engineering at the University of California San Diego. Prior to joining UC San Diego, he spent four years as a postdoctoral associate in the Department of Aeronautics and Astronautics and the Aerospace Computational Design Lab (ACDL) at the Massachusetts Institute of Technology (MIT). He received his MSc (2011) and PhD (2015) in mathematics from Virginia Tech. Prior to that, he studied mathematics in technology and mechanical engineering at the University of Karlsruhe (now KIT), Germany. He is a member of the Society for Industrial and Applied Mathematics (SIAM), an Associate Fellow of AIAA where he also serves on the Nondeterministic Approaches Technical Committees and a Senior Member of IEEE. He is a 2022 NSF CAREER Awardee and won a DoD Newton Award in 2020. He is an associate editor for the SIAM/ASA Journal of Uncertainty Quantification and IEEE Transactions on Automatic Control. His research is funded by the Office of Naval Research (ONR), the Air Force Office of Scientific Research (AFOSR), the Defense Advanced Research Projects Agency (DARPA), the Department of Energy (DOE), the National Science Foundation, as well as industrially through Samsung Electronics Co. and ASML. His research interests are to develop computational methods and numerical analysis for learning, control, design and uncertainty quantification of complex and large-scale systems. His research group has applied these methods to digital twins, rocket combustion, capillary wave turbulence, space weather, soft robotics, metal additive manufacturing, multidisciplinary design optimization, semiconductor manufacturing, radiation hardening of electronics and metamaterial design.