Geometric Structure-Preserving Model Reduction for Large-Scale Interconnected Systems: Part II
Abstract
Large-scale complex interconnected systems are ubiquitous in the DoD portfolio: Defense systems, aircraft, drones, smart robots, electronic circuits, Internet-of-Things, et cetera. Those systems are prohibitively expensive to simulate, therefore efficient surrogate models are needed for design, operation, and control. Complex interconnected systems have mathematical and physical structure. Ignoring this structure in surrogate modeling leads to unrealistic responses with potentially disastrous outcomes. The interconnection and coupling structure between subsystems needs to be maintained in a full-scale surrogate model for it to be meaningful and interpretable. Moreover, physical structure is often present at the subsystem level: a subsystem may be a Hamiltonian system, where the notion of passivity provides a systematic tool to generalize Lyapunov stability analysis of individual subsystems to the interconnected system. This proposal will build a new mathematical foundation to address the fundamental modeling paradigm: How can we approximate large-scale complex interconnected systems while retaining all important structures of the system? Which components and interconnections of the system can be modeled with reduced order so that the overall system response remains physically meaningful, accurate, and long-term predictive? We will start with developing the mathematical problem formulation to achieve this goal. Then, we will develop methods and requirements for structure preserving surrogate modeling that jointly approximate the interconnection structure of the largescale system and the physical structure of subsystems. This mathematical foundation will propel our long-term research goal: to obtain a complete framework for analysis, simulation, and reduced order modeling of large-scale complex interconnected systems, which will enable advanced design, operation, and control. This project synergistically leverages the expertise of PI Leok in geometric structure-preserving numerical integration, discrete geometric control of interconnected Lagrangian and Hamiltonian systems on nonlinear manifolds with the expertise of PI Kramer on model reduction of complex, large-scale models, both in the linear and nonlinear setting.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jun 25, 2021
- Source ID
- HQ00342010022
Entities
People
- Boris Krämer
Organizations
- Office of the Secretary of Defense
- University of California Regents
- Washington Headquarters Services