Parametric model order reduction with a small ℋ 2 $\mathcal {H}_{2}$ -error using radial basis functions

Predicting near optimal interpolation points for parametric model order reduction using regression models

“…Up to 2r linear systems of equations of size n have to be solved during the online phase for each reduced model, which can be of considerable computational cost. Benner et al suggest using intermediate models of moderate size but not necessarily optimal quality to compute the actual reduced model [10]. Here, the projection matrices computed in the training phase are reused to compute projection matrices V, W, which project the full system onto a subspace of order m > r. This intermediate model is then used to compute the projection matrices for an unknown set of parameters during the online phase.…”

Routh--type $L_2$ model reduction revisited

“…The model reduction problem has aroused a continual interest in the engineering community since the dawn of control and system theory [40,71], its importance being evident not only in system simulation and controller synthesis but also in many problems related to robustness and uncertainty issues. Indeed, despite the dramatic increase of computing capabilities that make the need for simplified models less compelling, the new challenges facing the control engineer have led to a revival of studies on this topic with particular emphasis on optimisation and algorithmic efficiency (see, e. g., [1,2,4,7,11,12], [14]- [59], [61,65,69,70]).…”

“…Besides the reduction methods based on the conservation of first-order information indices (e. g., coefficients of suitable series expansions), such as the classic Padé technique and its numerous variants [8,9] that are characterised by remarkable computational simplicity and ease of implementation, the methods based on second-order information indices (e. g., principal components, Hankel singular values, impulse-response energies) [16]- [19], [27,31,32,43,45,60,63], and on suitable quadratic criteria, such as the L 2 norm of the error [7,14], [21]- [24], [29], [33]- [35], [49,62], [66]- [68], [70,72], have enjoyed an increasing popularity since the late Seventies and early Eighties, and dedicated software has been developed for their implementation.…”

Model reduction for LPV systems based on approximate modal decomposition

“…Regarding parameter‐dependent systems, it is important to mention the family of parametric model reduction methods, see, eg, previous works. () Although these approaches show similar characteristics to the LPV model reduction, the problem they address is fundamentally different. The parametric model reduction starts from a parameterized set of large‐scale LTI systems.…”

“…The latter step is very difficult in general, 16 because the independently reduced (transformed and projected) local, LTI systems have to be transformed into a consistent state-space representation.Regarding parameter-dependent systems, it is important to mention the family of parametric model reduction methods, see, eg, previous works. [17][18][19][20] Although these approaches show similar characteristics to the LPV model reduction, the problem they address is fundamentally different. The parametric model reduction starts from a parameterized set of large-scale LTI systems.…”