Ellipsoidal state estimation for systems with interval uncertainties

Chabane, Sofiane Ben; Maniu, Cristina Stoica; Álamo, T.; Camacho, Eduardo F.; Dumur, Didier

doi:10.1109/cdc.2014.7039787

Cited by 8 publications

(4 citation statements)

References 13 publications

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“…Therefore, it is more natural to assume that these uncertainties are unknown-but-bounded variables with well-known bounds (20), and subsequently, it is of great interest to be able to characterize the set of all the possible state trajectories of (19), which are consistent with the uncertainty boxes (20). This set-membership state estimation problem has already been tackled in the literature [3][4][5]7,[9][10][11][13][14][15]28,29 where several geometrical forms (parallelotopes, ellipsoids, zonotopes, boxes, etc) are used to compute an enclosure of the state trajectories. The main idea of these approaches is relied on the prediction-correction procedure.…”

Section: Problem Statementmentioning

confidence: 99%

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Using set invariance to design robust interval observers for discrete‐time linear systems

Meslem

Loukkas

Martínez

2018

Intl J Robust & Nonlinear

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Summary Based on interval and invariant set computation, an interval version of the Luenberger state observer for uncertain discrete‐time linear systems is proposed in this work. This new interval observer provides a punctual estimation of the state vector and guaranteed bounds on the estimation error. An off‐line and an on‐line approach to characterize, in a guaranteed way, the estimation error are introduced. Compared with the existing approaches, the proposed interval observer design method is not restrictive in terms of required assumptions, complexity, and on‐line computation time. Furthermore, the convergence issue of the estimation error is well established and to reduce the conservatism of the estimated state enclosure induced by the bounded additive state disturbance and noise measurement, an H∞ method to compute the optimal observer gain is proposed. The performance of the proposed state estimation approach are highlighted on different illustrative examples.

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Section: Problem Statementmentioning

confidence: 99%

“…This set‐membership state estimation problem has already been tackled in the literature where several geometrical forms (parallelotopes, ellipsoids, zonotopes, boxes, etc) are used to compute an enclosure of the state trajectories. The main idea of these approaches is relied on the prediction‐correction procedure.…”

Section: Problem Statementmentioning

confidence: 99%

Using set invariance to design robust interval observers for discrete‐time linear systems

Meslem

Loukkas

Martínez

2018

Intl J Robust & Nonlinear

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“…For instance, modeling error, process and measurement noises can be assumed as unknown, but bounded inputs and only exogenous excitation like malicious cyber attacks can be viewed as completely unknown inputs. Thus, based on this decomposition, it is of great interest to extend the concept of set-valued state estimation [18][19][20][21][22][23][24][25][26][27][28][29] to design unknown input set-membership state estimators. This subject has already been considered in the literature.…”

Section: Introductionmentioning

confidence: 99%

State and unknown input set-valued estimation for uncertain linear discrete-time systems

Meslem

Hably

Raïssi

2023

Proceedings of the Institution of Mechanical Engineers, Part I:

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Set-valued algorithms are designed in this work to compute rigorous bounds of the unknown inputs of uncertain discrete-time linear systems. First, based on the classical full-order and reduced-order unknown input observers, non-conservative numerical schemes are proposed to characterize the reachable set of the estimation error. Then, by using these results, set-membership estimators of the unknown inputs are presented. Moreover, the results of these estimators can be merged together via set-intersection operators to obtain more accurate estimates.

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“…It offers less conservative results than the estimation obtained by the off-line P -radius-based zonotopic estimation method [14] due to the minimization of the ellipsoidal radius at each time instant. The ellipsoidal estimation was initially developed for linear systems with bounded perturbations and measurement noises in [27], while considering an interval evolution matrix in [28]. The originality of the present paper is to extend this method to the case of linear time-invariant systems with bounded perturbations, bounded measurement noises and interval uncertainties in both the evolution and observation matrices.…”

Section: Introductionmentioning

confidence: 99%

Ellipsoidal Set-Membership State Estimation for Multi-Output Systems with Interval Uncertainties

Chabane

Maniu

Álamo

et al. 2020

2020 European Control Conference (ECC)

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This paper presents a new online ellipsoidal guaranteed set-membership state estimation approach for Multi-Output linear systems with interval uncertainties, bounded perturbations and measurement noises. The ellipsoidal set containing the real state of the system is computed at each sample time. This approach consists in online minimizing the radius of the ellipsoidal state estimation set by solving a Linear Matrix Inequality optimization problem. Interval uncertainties are considered in both the evolution matrix and the observation matrix. An illustrative example is analyzed in order to show the advantages of the proposed approach.

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Ellipsoidal state estimation for systems with interval uncertainties

Cited by 8 publications

References 13 publications

Using set invariance to design robust interval observers for discrete‐time linear systems

Using set invariance to design robust interval observers for discrete‐time linear systems

State and unknown input set-valued estimation for uncertain linear discrete-time systems

Ellipsoidal Set-Membership State Estimation for Multi-Output Systems with Interval Uncertainties

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