Learning models from data: the set membership approach

Milanese, M.

doi:10.1109/acc.1998.694653

Cited by 12 publications

(6 citation statements)

References 41 publications

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“…Our approach therefore differs significantly from other methods presented in the literature that consist of validating [6], [4], [11], [8] or designing [10], [7] uncertainty regions containing the true system. In [6], [4], [11], and [8] and references therein, a method is proposed to decide whether a postulated region with bounded uncertainties is consistent with measured input-output data (the so-called model invalidation concept): [6] and [4] deal with frequency domain data while [11] and [8] tackle the same problem with time-domain data.…”

Section: Introductionmentioning

confidence: 98%

“…Our approach also differs significantly from the approach used in traditional set membership identification ( [10] and references therein), where a hard bound assumption is made on the noise and a known upper bound is required on the impulse response of the true system, leading to the identification of an uncertainty set around a nominal model. In [7], a method to identify an additive uncertainty region with a stochastic noise assumption is presented, but a known prior bound on the true system impulse response is again required.…”

Section: Introductionmentioning

confidence: 99%

“…For instance, in parameter and state estimation, the standard approach deals with random (specifically, Gaussian) perturbations, and least squares and Kalman filtering are the most popular tools for estimation under such assumptions. Later, the model of unknown-but-bounded perturbations was developed, which led to ellipsoidal techniques for estimation [14], [8], [10].…”

Section: Introductionmentioning

confidence: 99%

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A measure of robust stability for an identified set of parametrized transfer functions

Bombois¹,

Gevers²,

Scorletti³

2000

IEEE Trans. Automat. Contr.

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In this paper, we define a measure of robustness for a set of parameterized transfer functions as delivered by classical prediction error identification and that contains the true system at a prescribed probability level. This measure of robustness is the worst case Vinnicombe distance between the model and the plants in the uncertainty region. We show how it can be computed exactly using LMI-based optimization. In addition, we show that this measure is directly connected to the size of the set of controllers that are guaranteed to stabilize all plants in the uncertainty region, i.e., the smaller the worst case Vinnicombe distance for an uncertainty region, the larger the set of model-based controllers that are guaranteed to stabilize all systems in this uncertainty region.

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Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A measure of robust stability for an identified set of parametrized transfer functions

Bombois¹,

Gevers²,

Scorletti³

2000

IEEE Trans. Automat. Contr.

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show abstract

“…The set of unfalsified models often becomes very complicated and one important research topic has been to find simplified characterizations using outer-and inner-bounding techniques (Milanese & Vicino, 1991). We refer to Milanese (1998) and Milanese, Norton, Piet-Lahanier, and Walter (1996) and references therein for further details on set-membership identification.…”

Section: Set-membership Identificationmentioning

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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“…Otherwise increase the model error model complexity until it is unfalsified by the data. Nonparametric model error models can also be used [20,24,27].…”

Section: Model Error Modelingmentioning

confidence: 99%

Comparing different approaches to model error modeling in robust identification

2002

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Identification for robust control must deliver not only a nominal model, but also a reliable estimate of the uncertainty associated with the model. This paper addresses recent approaches to robust identification, that aim at dealing with contributions from the two main uncertainty sources: unmodeled dynamics and noise affecting the data. In particular, the following methods are considered: non-stationary Stochastic Embedding, Model Error Modeling based on prediction error methods and Set Membership Identification. Moreover, we show how Set Membership Identification can be embedded into a Model Error Modeling framework. Model validation issues are easily addressed in the proposed framework. It is shown how the computation of the minimum noise bound for which a nominal model is not falsified by input-output data, can be used as a rationale for selecting an appropriate model class in the set membership setting. For all three methods, uncertainty is evaluated in terms of the frequency response, so that it can be handled by H ∞ control techniques. An example, where a nontrivial undermodeling is ensured by the presence of a nonlinearity in the system generating the data, is presented to compare the different methods.

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Learning models from data: the set membership approach

Cited by 12 publications

References 41 publications

A measure of robust stability for an identified set of parametrized transfer functions

A measure of robust stability for an identified set of parametrized transfer functions

From experiment design to closed-loop control

Comparing different approaches to model error modeling in robust identification

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