Model Order Reduction from Data with Certification

• DOI: 10.48550/arxiv.2502.01094
• Publication Date: 2025-02-03
• Authors: Behrad Samari; A. Nejati; Abolfazl Lavaei
• Keywords: FOS: Electrical engineering, electronic engineering, information engineering; Systems and Control (eess.SY); Electrical Engineering and Systems Science - Systems and Control

Model order reduction (MOR) involves offering low-dimensional models that effectively approximate the behavior of complex high-order systems. Due to potential model complexities and computational costs, designing controllers for high-dimensional systems with behaviors can be challenging, rendering MOR a practical alternative achieve results closely resemble those original To construct such effective reduced-order (ROMs), existing literature generally necessitates precise knowledge systems, which is often unavailable in real-world scenarios. This paper introduces data-driven scheme ROMs dynamical unknown mathematical models. Our methodology leverages data establishes similarity relations between output trajectories their via notion simulation functions (SFs), capable formally quantifying closeness. this, under rank condition readily fulfillable using data, we collect only two input-state from both SFs, while correctness guarantees. We demonstrate proposed derived leveraged controller synthesis endeavors ensuring high-level logic properties over showcase our findings across range benchmark scenarios involving various physical demonstrating enforcement diverse properties.