145 research outputs found
Inexact Solves in Interpolatory Model Reduction
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
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
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
Pseudo-Optimal Reduction of Structured DAEs by Rational Interpolation
In this contribution, we extend the concept of inner product
and pseudo-optimality to dynamical systems modeled by
differential-algebraic equations (DAEs). To this end, we derive projected
Sylvester equations that characterize the inner product in
terms of the matrices of the DAE realization. Using this result, we extend the
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 defined by
poles and input residual directions. Necessary and sufficient conditions for
pseudo-optimality are derived using the new formulation of the
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
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 -inspired
algorithm for effectively choosing the interpolation points and tangential
directions. The algorithm leads a reduced port-Hamiltonian model that satisfies
a subset of -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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