Nu-gap model reduction in the frequency domain

Sootla, Aivar

doi:10.1109/acc.2011.5991242

Cited by 3 publications

(4 citation statements)

References 30 publications

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“…The -gap metric has been applied to areas such as system identification [8][9][10], model/controller reduction [11,12], and adaptive control employing multiple models [13].…”

Section: Introductionmentioning

confidence: 99%

Identification of an LFT uncertainty model by minimizing the ν-gap metric

Häggblom

2014

2014 European Control Conference (ECC)

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An uncertainty model in the form of a linear fractional transformation (LFT) is composed of a nominal model augmented by an uncertainty description. The size of the uncertainty required to cover a given set of models depends not only on the set of models, but also on the nominal model. Thus, the size of the uncertainty can be minimized by choosing the nominal model optimally according to some metric. If the uncertainty model is to be used for control design, a suitable metric is the -gap metric. It is shown that the optimal solution in terms of the -gap metric has to satisfy a bilinear matrix inequality (BMI) for every model in the model set. To solve this nonconvex optimization problem, the BMIs are linearized to enable an iterative solution constrained by linear matrix inequalities (LMIs), where each iteration is a convex optimization problem. It is proved that the iteration converges to the optimal solution satisfying the BMIs. Because the solution is obtained as the frequency response at selected frequencies, the final model is determined by fitting a model to the frequency responses. A state-space model is used because the fitting can then easily be done subject to the same BMIs/LMIs to guarantee an optimal model. The procedure is illustrated by an application to uncertainty modeling of the product composition dynamics of a distillation column.

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“…The -gap metric has been applied to areas such as system identification [8][9][10], model/controller reduction [11,12], and adaptive control employing multiple models [13].…”

Section: Introductionmentioning

confidence: 99%

Identification of an LFT uncertainty model by minimizing the ν-gap metric

Häggblom

2014

2014 European Control Conference (ECC)

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“…First, it is well known that the ν-gap metric does not account for any performance objectives of a closed-loop system. Hence, if the application at hand includes also robust performance specifications, and since our optimization problem is SDP based, one could easily add additional performance constraints by ensuring that the appropriate sensitivity functions are all well behaved, see for example [23]. Second, our approach could potentially be combined with other LMI based applications in the ν-gap metric, such as the recent and powerful results related to model order reduction [23], [24], [25].…”

Section: Introductionmentioning

confidence: 97%

“…Hence, if the application at hand includes also robust performance specifications, and since our optimization problem is SDP based, one could easily add additional performance constraints by ensuring that the appropriate sensitivity functions are all well behaved, see for example [23]. Second, our approach could potentially be combined with other LMI based applications in the ν-gap metric, such as the recent and powerful results related to model order reduction [23], [24], [25]. Our algorithm is based on a three-step modus operandi: (i) an initial central transfer function is first computed through LMI relaxations of a nonconvex problem, on the basis of matrix Sum-OfSquares (SOS) decompositions, followed by (ii) a non-linear SDP based refinement, and finally (iii) the actual computation of the ν-gap using the Kalman-Yakubovich-Popov (KYP) Lemma.…”

Section: Introductionmentioning

confidence: 99%

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Nu-gap metric a sum-of-squares and linear matrix inequality approach

Taamallah¹

2014

2014 18th International Conference on System Theory, Control and Computing (ICSTCC)

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The nu-gap metric represents a good measure of the distance between systems in a closed-loop setting. The purpose of this paper is to present a novel method to compute the nu-gap using a Semi-Definite Programming (SDP) procedure. Our approach is formulated through a three-step modus operandi: (i) first an initial central transfer function is computed through Linear Matrix Inequality (LMI) relaxations of a nonconvex problem, on the basis of matrix Sum-Of-Squares (SOS) decompositions, followed by (ii) a non-linear LMI-based refinement, and finally (iii) the actual computation of the nugap using the Kalman-Yakubovich-Popov (KYP) Lemma. We illustrate the practicality of the proposed method on numerical examples.

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