Set-Membership Error-in-Variables Identification Through Convex Relaxation Techniques

Cerone, V.; Piga, Dario; Regruto, D.

doi:10.1109/tac.2011.2168073

Cited by 67 publications

(44 citation statements)

References 15 publications

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“…In this case, the nature of regressor quantization and the characterization of noise in terms of deterministic bounds, make the problem amenable to the set membership approach, although important developments have been made also in the stochastic setting (see, e.g., [9], [12]- [14]) or even in a mixed stochastic/deterministic framework [15], [16]. When considering ARX models in this quantized information setting [17], or OE and EiV models in general [18], [19], one is faced with a problem with perturbed regressors. In these cases, the nice property of convexity of the FPS is generally lost, so that almost all of the methods and techniques proposed for the standard linear regression formulation do not apply.…”

Section: Introductionmentioning

confidence: 99%

“…Still in an OE context, in [28] of both approaches is that the approximation procedure does not explicitly account for regressor sequential correlation, giving rise to quite conservative results whenever such correlation is present. More recently, in [19], [29] an EiV formulation has been considered in which all the regressor variables are subject to bounded noises. For this general setting, a procedure is provided to derive parameter uncertainty intervals, i.e., bounds on the nonconvex FPS, based on a sequence of problem relaxations leading to linear matrix inequalities and using the sparsity of the resulting relaxed problems.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Feasible Parameter Set Approximation for Linear Models with Bounded Uncertain Regressors

Casini

Garulli

Vicino

2014

IEEE Trans. Automat. Contr.

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Nonconvex feasible parameter sets are encountered in set membership identification whenever the regressor vector is affected by bounded uncertainty. This occurs for example when considering standard output error models, or when the available measurements are provided by binary or quantized sensors. In this paper, a unifying framework is proposed to deal with several identification problems involving a nonconvex feasible parameter set and a procedure is proposed for approximating the minimum volume orthotope containing the feasible set. The procedure exploits different relaxations for autoregressive and input parameters, based on the solution of a sequence of linear programming problems. The proposed technique is shown to provide tight bounds in some special cases. Moreover, it is extended to cope with bounds not aligned with the parameter coordinates, in order to obtain polytopic approximations of the feasible set. A number of numerical tests on randomly generated models and data sets demonstrates the accuracy of the computed set approximations. Index Terms-Errors-in-variables, output error models, quantized measurements, set membership identification.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Feasible Parameter Set Approximation for Linear Models with Bounded Uncertain Regressors

Casini

Garulli

Vicino

2014

IEEE Trans. Automat. Contr.

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“…The estimate θ 1 c computed by solving (29) is the so-called ℓ p -Chebyshev center of D θ 1 , also called central estimate in the SM literature. In the case p = ∞, the central estimate is the center of the minimum-volume-box outerbounding D θ 1 and can be computed by exploiting the convex relaxation approach proposed in Cerone, Piga, and Regruto (2012). Although the central estimate provides the minimum of the worst-case estimation error, it may show some undesirable features in this case, since the set D θ 1 is nonconvex.…”

Section: A Bounded-error Approach To Laser Parameter Estimationmentioning

confidence: 99%

Set-membership estimation of fiber laser physical parameters from input–output power measurements

2015

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“…Most of current error-in-variables methods are aimed at linear systems (see [18], [4] and references therein). An exception is the work in [6], extending the idea of [15] to cases with measurement noise.…”

Section: Introductionmentioning

confidence: 99%

A convex optimization approach to semi-supervised identification of switched ARX systems

Cheng

Wang

Sznaier

2014

53rd IEEE Conference on Decision and Control

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This paper proposes a general convex framework for robustly identifying discrete-time affine hybrid systems from measurements contaminated by noise (both process and measurement) and outliers. Our main result shows that this problem can be formulated as a constrained polynomial optimization, for which a monotonically convergent sequence of tractable convex relaxations can be obtained by exploiting recent developments in sparse polynomial optimization. A salient feature of the proposed framework is its ability to incorporate existing a-priori information about the noise, co-ocurrences, or the switching sequence. These results are illustrated with several examples showing the ability of the proposed approach to make effective use of this additional information. 53rd IEEE Conference on Decision and Control

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Set-Membership Error-in-Variables Identification Through Convex Relaxation Techniques

Cited by 67 publications

References 15 publications

Feasible Parameter Set Approximation for Linear Models with Bounded Uncertain Regressors

Feasible Parameter Set Approximation for Linear Models with Bounded Uncertain Regressors

Set-membership estimation of fiber laser physical parameters from input–output power measurements

A convex optimization approach to semi-supervised identification of switched ARX systems

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