145 research outputs found

    Inexact Solves in Interpolatory Model Reduction

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    We investigate the use of inexact solves for interpolatory model reduction and consider associated perturbation effects on the underlying model reduction problem. We give bounds on system perturbations induced by inexact solves and relate this to termination criteria for iterative solution methods. We show that when a Petrov-Galerkin framework is employed for the inexact solves, the associated reduced order model is an exact interpolatory model for a nearby full-order system; thus demonstrating backward stability. We also give evidence that for \h2-optimal interpolation points, interpolatory model reduction is robust with respect to perturbations due to inexact solves. Finally, we demonstrate the effecitveness of direct use of inexact solves in optimal H2{\mathcal H}_2 approximation. The result is an effective model reduction strategy that is applicable in realistically large-scale settings.Comment: 42 pages, 5 figure

    Interpolatory Methods for Generic BizJet Gust Load Alleviation Function

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    The paper's main contribution concerns the use of interpolatory methods to solve end to end industrial control problems involving complex linear dynamical systems. More in details, contributions show how the rational data and function interpolation framework is a pivotal tool (i) to construct (frequency-limited) reduced order dynamical models appropriate for model-based control design and (ii) to accurately discretise controllers in view of on-board computer-limited implementation. These contributions are illustrated along the paper through the design of an active feedback gust load alleviation function, applied on an industrial generic business jet aircraft use-case. The closed-loop validation and performances evaluation are assessed through the use of an industrial dedicated simulator and considering certification objectives. Although application is centred on aircraft applications, the method is not restrictive and can be extended to any linear dynamical systems.Comment: 23 pages, 9 figures, submitted to journa

    H2\mathcal{H}_2 Pseudo-Optimal Reduction of Structured DAEs by Rational Interpolation

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    In this contribution, we extend the concept of H2\mathcal{H}_2 inner product and H2\mathcal{H}_2 pseudo-optimality to dynamical systems modeled by differential-algebraic equations (DAEs). To this end, we derive projected Sylvester equations that characterize the H2\mathcal{H}_2 inner product in terms of the matrices of the DAE realization. Using this result, we extend the H2\mathcal{H}_2 pseudo-optimal rational Krylov algorithm for ordinary differential equations to the DAE case. This algorithm computes the globally optimal reduced-order model for a given subspace of H2\mathcal{H}_2 defined by poles and input residual directions. Necessary and sufficient conditions for H2\mathcal{H}_2 pseudo-optimality are derived using the new formulation of the H2\mathcal{H}_2 inner product in terms of tangential interpolation conditions. Based on these conditions, the cumulative reduction procedure combined with the adaptive rational Krylov algorithm, known as CUREd SPARK, is extended to DAEs. Important properties of this procedure are that it guarantees stability preservation and adaptively selects interpolation frequencies and reduced order. Numerical examples are used to illustrate the theoretical discussion. Even though the results apply in theory to general DAEs, special structures will be exploited for numerically efficient implementations

    Structure-preserving tangential interpolation for model reduction of port-Hamiltonian Systems

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    Port-Hamiltonian systems result from port-based network modeling of physical systems and are an important example of passive state-space systems. In this paper, we develop the framework for model reduction of large-scale multi-input/multi-output port-Hamiltonian systems via tangential rational interpolation. The resulting reduced-order model not only is a rational tangential interpolant but also retains the port-Hamiltonian structure; hence is passive. This reduction methodology is described in both energy and co-energy system coordinates. We also introduce an H2\mathcal{H}_2-inspired algorithm for effectively choosing the interpolation points and tangential directions. The algorithm leads a reduced port-Hamiltonian model that satisfies a subset of H2\mathcal{H}_2-optimality conditions. We present several numerical examples that illustrate the effectiveness of the proposed method showing that it outperforms other existing techniques in both quality and numerical efficiency
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