Browsing by Author "Benner, Peter"

Now showing 1 - 3 of 3
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    Interpolatory projection methods for parameterized model reduction
    Baur, Ulrike; Beattie, Christopher A.; Benner, Peter; Gugercin, Serkan (Siam Publications, 2011)
    We provide a unifying projection-based framework for structure-preserving interpolatory model reduction of parameterized linear dynamical systems, i.e., systems having a structured dependence on parameters that we wish to retain in the reduced-order model. The parameter dependence may be linear or nonlinear and is retained in the reduced-order model. Moreover, we are able to give conditions under which the gradient and Hessian of the system response with respect to the system parameters is matched in the reduced-order model. We provide a systematic approach built on established interpolatory H(2) optimal model reduction methods that will produce parameterized reduced-order models having high fidelity throughout a parameter range of interest. For single input/single output systems with parameters in the input/output maps, we provide reduced-order models that are optimal with respect to an H(2) circle times L(2) joint error measure. The capabilities of these approaches are illustrated by several numerical examples from technical applications.
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    Structure-preserving interpolation of bilinear control systems
    Benner, Peter; Gugercin, Serkan; Werner, Steffen W. R. (2021-06)
    In this paper, we extend the structure-preserving interpolatory model reduction framework, originally developed for linear systems, to structured bilinear control systems. Specifically, we give explicit construction formulae for the model reduction bases to satisfy different types of interpolation conditions. First, we establish the analysis for transfer function interpolation for single-input single-output structured bilinear systems. Then, we extend these results to the case of multi-input multi-output structured bilinear systems by matrix interpolation. The effectiveness of our structure-preserving approach is illustrated by means of various numerical examples.
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    ℋ₂-Quasi-Optimal Model Order Reduction for Quadratic-Bilinear Control Systems
    Benner, Peter; Goyal, P.; Gugercin, Serkan (2017-05-16)
    We investigate the optimal model reduction problem for large-scale quadratic-bilinear (QB) control systems. Our contributions are threefold. First, we discuss the variational analysis and the Volterra series formulation for QB systems. We then define the H2-norm for a QB system based on the kernels of the underlying Volterra series and also propose a truncated H2-norm. Next, we derive first-order necessary conditions for an optimal approximation, where optimality is measured in term of the truncated H2-norm of the error system. We then propose an iterative model reduction algorithm, which upon convergence yields a reduced-order system that approximately satisfies the newly derived optimality conditions. We also discuss an efficient computation of the reduced Hessian, using the special Kronecker structure of the Hessian of the system. We illustrate the efficiency of the proposed method by means of several numerical examples resulting from semi-discretized nonlinear partial differential equations and show its competitiveness with the existing model reduction schemes for QB systems such as moment-matching methods and balanced truncation.