2025/05/05 by Sean Reiter, Ion Victor Gosea, Reiter, Sean +5 · 2 citations
Engineering · Physics and Astronomy · #34C20 #41A05 #49K15 #65F99 #65J05 #93A15 #93C10 #93C80 #Dynamical Systems (math.DS) #FOS: Electrical engineering #FOS: Mathematics #Fault Detection and Control Systems #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Real-time simulation and control systems #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2505.03057
openalex publication_date 2025/05/05 · openalex created_date 2025/10/16 · openalex updated_date 2026/08/01
This paper addresses the H2-optimal approximation of linear dynamical systems with quadratic-output functions, also known as linear quadratic-output systems. Our major contributions are threefold. First, we derive interpolatory first-order optimality conditions for the linear quadratic-output H2 minimization problem. These conditions correspond to the mixed-multipoint tangential interpolation of the full-order linear- and quadratic-output transfer functions, and generalize the Meier-Luenberger optimality framework for the H2-optimal model reduction of linear time-invariant systems. Second, given the optimal interpolation data, we show how to enforce the interpolatory optimality conditions explicitly by Petrov-Galerkin projection of the full-order model. Third, to find the optimal interpolation data, we build on this projection framework and propose a generalization of the iterative rational Krylov algorithm for the H2-optimal model reduction of linear quadratic-output systems, called LQO-IRKA. Upon convergence, LQO-IRKA produces reduced linear quadratic-output systems that satisfy the interpolatory optimality conditions. The method only requires solving shifted linear systems and matrix-vector products, thus making it suitable for large-scale problems. Numerical examples are included to illustrate the effectiveness of the proposed method.