Data-driven balanced truncation for second-order systems with generalized proportional damping

2025/06/11 by Reiter, Sean, Werner, Steffen W. R. · 1 citation
#37N35 #65F55 #93A15 #93B15 #93C57 #Dynamical Systems (math.DS) #FOS: Electrical engineering #FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · doi:10.48550/arxiv.2506.10118

Abstract

Structured reduced-order modeling is a central component in the computer-aided design of control systems in which cheap-to-evaluate low-dimensional models with physically meaningful internal structures are computed. In this work, we develop a new approach for the structured data-driven surrogate modeling of linear dynamical systems described by second-order time derivatives via balanced truncation model-order reduction. The proposed method is a data-driven reformulation of position-velocity balanced truncation for second-order systems and generalizes the quadrature-based balanced truncation for unstructured first-order systems to the second-order case. The computed surrogates encode a generalized proportional damping structure, and the damping coefficients are inferred solely from data by minimizing a least-squares error over the coefficients. Several numerical examples demonstrate the effectiveness of the proposed method.

Citations

• Data-driven balanced truncation for second-order systems via the approximate Gramians
• Second-order AAA algorithms for structured data-driven modeling
• Model reduction for second-order systems with inhomogeneous initial conditions
• Hamiltonian Operator Inference: Physics-preserving Learning of Reduced-order Models for Canonical Hamiltonian Systems
• Data-driven balancing of linear dynamical systems
• Data-Driven Identification of Rayleigh-Damped Second-Order Systems
• Truncated balanced realization of a stable non-minimal state-space system
• Principal component analysis in linear systems: Controllability, observability, and model reduction

Cited by

• Data-driven balanced truncation for linear systems with quadratic outputs

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