Identification of probabilistic system uncertainty regions by explicit evaluation of bias and variance errors

Hakvoort, R.G.; Hof, Paul M.J. Van den

doi:10.1109/9.649691

Cited by 64 publications

(33 citation statements)

References 43 publications

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“…However, colored noise can be treated as well (see (Hakvoort and den Hof, 1997)). As proposed in (Hakvoort and den Hof, 1997), the reduced-order model structure that we will use for the identification is linear in the parameter i.e.…”

Section: Pe Identification Aspectsmentioning

confidence: 99%

“…In this case, the modeling error is made up of two contributions: a variance contribution due to the noise (such as in (1)) and a bias contribution due to the undermodeling. If the model structure is chosen linear in the parameter vector, both contributions can be a-priori estimated by upperbounds α(ω, u)a n dβ(ω, u) depending on the tobe-determined input signal (Hakvoort and den Hof, 1997). This leads to the following experiment design problem:…”

Section: Introductionmentioning

confidence: 99%

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Cheapest Identification Experiment With Guaranteed Accuracy in the Presence of Undermodeling

Bombois

Gilson

2006

IFAC Proceedings Volumes

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Section: Pe Identification Aspectsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Cheapest Identification Experiment With Guaranteed Accuracy in the Presence of Undermodeling

Bombois

Gilson

2006

IFAC Proceedings Volumes

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“…Another contribution to the frequency domain bounding of ellipsoidal parameter sets is Devilbiss and Yurkovich (1998). Confidence bounds in the frequency domain, taking undermodelling explicitly into account, for the instrumental variable method are developed in Hakvoort and Van den Hof (1997).…”

Section: Outerbounding the Set Of Unfalsified Modelsmentioning

confidence: 99%

From experiment design to closed-loop control

2005

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The links between identification and control are examined. The main trends in this research area are summarized, with particular focus on the design of low complexity controllers from a statistical perspective. It is argued that a guiding principle should be to model as well as possible before any model or controller simplifications are made as this ensures the best statistical accuracy. This does not necessarily mean that a full-order model always is necessary as well designed experiments allow for restricted complexity models to be near-optimal. Experiment design can therefore be seen as the key to successful applications. For this reason, particular attention is given to the interaction between experimental constraints and performance specifications.

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“…Much work has been devoted to the problem of separating the two effects in (3), e.g. [4], [6], [11], [12], [5], [1]. Often the model error is assumed to be linear (i.e.…”

Section: ε(T) = Y(t) −ĝ(Q)u(t)mentioning

confidence: 99%

Robustness guarantees for linear control designs with an estimated nonlinear model error model

Glad

Helmersson

Ljung

2004

Intl J Robust & Nonlinear

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Much attention in robust identification and control has been focused on linear low order models approximating high order linear systems. We consider the more realistic situation with a linear model approximating a non-linear system. We describe how a non-linear model error model can be developed, that allows a complete linear design process that results in a closed loop system with performance robustness guarantees (in terms of gain from disturbance to output) against the nonlinear error. Clearly the design can be successful only if the linear model is a reasonably good approximation of the system. A particular aspect of the design process is to define a workable definition of "practical stability" for robust control design, with possible nonlinear model errors. We use affine norms for that purpose. Abstract. Much attention in robust identification and control has been focused on linear low order models approximating high order linear systems. We consider the more realistic situation with a linear model approximating a non-linear system. We describe how a non-linear model error model can be developed, that allows a complete linear design process that results in a closed loop system with performance robustness guarantees (in terms of gain from disturbance to output) against the nonlinear error. Clearly the design can be successful only if the linear model is a reasonably good approximation of the system. A particular aspect of the design process is to define a workable definition of "practical stability" for robust control design, with possible nonlinear model errors. We use affine norms for that purpose. Keywords

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Identification of probabilistic system uncertainty regions by explicit evaluation of bias and variance errors

Cited by 64 publications

References 43 publications

Cheapest Identification Experiment With Guaranteed Accuracy in the Presence of Undermodeling

Cheapest Identification Experiment With Guaranteed Accuracy in the Presence of Undermodeling

From experiment design to closed-loop control

Robustness guarantees for linear control designs with an estimated nonlinear model error model

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