On the State-Space Realization of LPV Input-Output Models: Practical Approaches

Tóth, Roland; Abbas, Hossam S.; Werner, Herbert

doi:10.1109/tcst.2011.2109040

Cited by 99 publications

(147 citation statements)

References 29 publications

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“…Additionally, realization theory of LPV models and LPV modeling of nonlinear systems requires that the model coefficients not only depend on the instantaneous values of p (static dependence) but also on its time-shifted versions (dynamic dependence) [9]. Thus, estimating LPV-ARX models with dynamic dependence is often required for obtaining accurate models of the underlying system.…”

Section: Introductionmentioning

confidence: 99%

Model structure learning: A support vector machine approach for LPV linear-regression models

Tóth

Laurain

Zheng

et al. 2011

IEEE Conference on Decision and Control and European Control Conference

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Section: Introductionmentioning

confidence: 99%

Model structure learning: A support vector machine approach for LPV linear-regression models

Tóth

Laurain

Zheng

et al. 2011

IEEE Conference on Decision and Control and European Control Conference

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“…where J p id can be either [14] for details), while Property 2 follows from the structure of the set D in (6) (see [9], [11] for details).…”

Section: Computation Of θ * and Related Discussionmentioning

confidence: 99%

“…Unfortunately, as shown in [12], exact state-space realization leads to an LPV-SS model with a dynamic dependence of A, B, C, D on λ, thus increasing complexity of the control synthesis. Indeed, an approximate SS realization of the I/O model (1a) with static dependence of A, B, C, D on the scheduling parameter is to be preferred in order to use common LPV control design tools [14].…”

Section: State-space Realization-oriented Selection Of a Single mentioning

confidence: 99%

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Minimal LPV state-space realization driven set-membership identification

Cerone

Piga

Regruto

et al. 2012

2012 American Control Conference (ACC)

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Abstract-Set-membership identification algorithms have been recently proposed to derive linear parameter-varying (LPV) models in input-output form, under the assumption that both measurements of the output and the scheduling signals are affected by bounded noise. In order to use the identified models for controller synthesis, linear time-invariant (LTI) realization theory is usually applied to derive a statespace model whose matrices depend statically on the scheduling signals, as required by most of the LPV control synthesis techniques. Unfortunately, application of the LTI realization theory leads to an approximate state-space description of the original LPV input-output model. In order to limit the effect of the realization error, a new set-membership algorithm for identification of input/output LPV models is proposed in the paper. A suitable nonconvex optimization problem is formulated to select the model in the feasible set which minimizes a suitable measure of the state-space realization error. The solution of the identification problem is then derived by means of convex relaxation techniques.

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“…(4) is not commutative over the p-dependent coefficients a i and b j , the involved realization theory is more complicated than in the LTI case and often introduces complicated rational dynamic dependence on p in the resulting SS forms [Tóth et al (2011e)]. Even if there exist some strategies to avoid such complications in specific situations (see [Tóth et al (2011a)]), the burden of the realization is likely to rise difficulties in applications.…”

Section: Perspectives Of Series-expansion Modelsmentioning

confidence: 99%