Estimation of parameter bounds from bounded-error data: a survey

Walter, Éric; Piet-Lahanier, Hélène

doi:10.1016/0378-4754(90)90002-z

Cited by 289 publications

(103 citation statements)

References 57 publications

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“…P (4 n ) ; where P (4 n ) is the set of all subsets of 4 n ; is inclusion monotonic if (21) Proof: The proof for (i) is trivial, and we shall only give a proof for (ii). First, recall that if a 1 ; : : : ; a n ; b 1 ; : : : ; b n are Boolean numbers, then, n ; i=1 (a i + b i ) = (a 1 a 2 : : : a n¡1 a n ) + (a 1 a 2 : : : a n¡1 b n ) + ¢ ¢ ¢ + (b 1 b 2 : : : b n¡1 b n ) : (22) Now, since in Boolean algebra, a + b¸a, (22) However, an exact procedure to evaluate it via the computation of a disjunctive form may become too complex when the number m of sets increases, because this disjunctive form is usually longer than the initial form.…”

Section: Denitionsmentioning

confidence: 99%

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Guaranteed robust nonlinear minimax estimation

Jaulin

Walter

2002

IEEE Trans. Automat. Contr.

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Minimax parameter estimation aims at characterizing the set of all values of the parameter vector that minimize the largest absolute deviation between experimental data and corresponding model outputs. However, minimax estimation is well known to be extremely sensitive to outliers in the data resulting, e.g., of sensor failures. In this paper, a new method is proposed to robustify minimax estimation by allowing a prespecied number of absolute deviations to become arbitrarily large without modifying the estimates. By combining tools of interval analysis and constraint propagation, it becomes possible to compute the corresponding minimax estimates in an approximate but guaranteed way, even when the model output is nonlinear in its parameters. The method is illustrated on a problem where the parameters are not globally identiable, which demonstrates its ability to deal with the case where the minimax solution is not unique.

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Section: Denitionsmentioning

confidence: 99%

“…Moreover, the corresponding largest absolute deviation± is a lower bound for ±, which provides useful information to anyone interested in bounded-error parameter estimation. (See [ [18], [19], [21], [16], [5], [14] and the references therein).…”

Section: Introductionmentioning

confidence: 99%

Guaranteed robust nonlinear minimax estimation

Jaulin

Walter

2002

IEEE Trans. Automat. Contr.

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“…The issue of computing the setĜ(k) of parameters θ compatible with a data set on the basis of a known bound measurement error has received a good deal of attention [10], [12], [15], [16]. Practically, the polyhedronĜ(k) is computed as the intersection of 2k half spaces in the parameter space defined by equations of the form:…”

Section: Computation Of the Unfalsified Setsmentioning

confidence: 99%

Strong robustness in multi‐phase adaptive control: the basic scheme

Cadic

Polderman

2004

Adaptive Control & Signal

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This paper introduces the general structure of adaptive control systems based on strong robustness. This adaptive approach splits into two phases. In the first phase, effort is put on identification until enough information is obtained in order to design a controller stabilizing the actual system. This is achieved if the input sequence is computed in such a way that the uncertainty on the system parameters to be controlled decreases sufficiently fast. Then, in the second phase, emphasis is shifted to control.

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“…In this context, all parameters consistent with the measurements, the error bounds and the assumed model structure, are feasible solutions of the identification problem. The interested reader can find further details on this approach in a number of survey papers (see, e.g., [8], [9]), in the book edited by Milanese et al [10], and the special issues edited by Norton [11], [12].…”

Section: Introductionmentioning

confidence: 99%

Bounding the parameters of linear systems with stability constraints

Cerone

Piga

Regruto

2010

Proceedings of the 2010 American Control Conference

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Abstract-Identification of linear systems, a priori known to be stable, from input output measurements corrupted by bounded noise is considered in the paper. A formal definition of the feasible parameter set is provided, taking explicitly into account prior information on system stability. On the basis of a detailed analysis of the geometrical structure of the feasible set, convex relaxation techniques are presented to solve nonconvex optimization problems arising in the computation of the parameters uncertainty intervals. Properties of the computed relaxed bounds are discussed. A simulated example is presented to show the effectiveness of the proposed technique.

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Estimation of parameter bounds from bounded-error data: a survey

Cited by 289 publications

References 57 publications

Guaranteed robust nonlinear minimax estimation

Guaranteed robust nonlinear minimax estimation

Strong robustness in multi‐phase adaptive control: the basic scheme

Bounding the parameters of linear systems with stability constraints

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