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Optimization-based parametric model order reduction via \(\mathcal{H}_2\otimes\mathcal{L}_2\) first-order necessary conditions. (English) Zbl 1492.65227

Summary: In this paper, we generalize existing frameworks for \(\mathcal{H}_2\otimes\mathcal{L}_2\)-optimal model order reduction to a broad class of parametric linear time-invariant systems. To this end, we derive first-order necessary optimality conditions for a class of structured reduced-order models and then, building on those, propose a stability-preserving optimization-based method for computing locally \(\mathcal{H}_2\otimes\mathcal{L}_2\)-optimal reduced-order models. We also make a theoretical comparison to existing approaches in the literature and, in numerical experiments, show how our new method, with reasonable computational effort, produces stable optimized reduced-order models with significantly lower approximation errors.

MSC:

65L99 Numerical methods for ordinary differential equations
15A24 Matrix equations and identities
46N10 Applications of functional analysis in optimization, convex analysis, mathematical programming, economics
65K05 Numerical mathematical programming methods
65Y20 Complexity and performance of numerical algorithms
93-08 Computational methods for problems pertaining to systems and control theory
93A15 Large-scale systems
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References:

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