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Semi‐active ℋ ∞ damping optimization by adaptive interpolation
Author(s) -
Tomljanović Zoran,
Voigt Matthias
Publication year - 2020
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.2300
Subject(s) - interpolation (computer graphics) , mathematical optimization , mathematics , norm (philosophy) , parametric statistics , bilinear interpolation , inverse quadratic interpolation , heuristics , transfer function , computer science , spline interpolation , trilinear interpolation , artificial intelligence , motion (physics) , statistics , electrical engineering , engineering , political science , law
Summary In this work we consider the problem of semi‐active damping optimization of mechanical systems with fixed damper positions. Our goal is to compute a damping that is locally optimal with respect to theℋ ∞‐norm of the transfer function from the exogenous inputs to the performance outputs. We make use of a new greedy method for computing theℋ ∞‐norm of a transfer function based on rational interpolation. In this paper, this approach is adapted to parameter‐dependent transfer functions. The interpolation leads to parametric reduced‐order models that can be optimized more efficiently. At the optimizers we then take new interpolation points to refine the reduced‐order model and to obtain updated optimizers. In our numerical examples we show that this approach normally converges fast and thus can highly accelerate the optimization procedure. Another contribution of this work is heuristics for choosing initial interpolation points.