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Article

Union and Intersection Operators for Thick Ellipsoid State Enclosures: Application to Bounded-Error Discrete-Time State Observer Design

ENSTA Bretagne, Lab-STICC, 29806 Brest, France
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Academic Editor: Mircea-Bogdan Rada
Algorithms 2021, 14(3), 88; https://doi.org/10.3390/a14030088
Received: 3 March 2021 / Revised: 9 March 2021 / Accepted: 11 March 2021 / Published: 14 March 2021
(This article belongs to the Special Issue Algorithms for Reliable Estimation, Identification and Control II)
Thick ellipsoids were recently introduced by the authors to represent uncertainty in state variables of dynamic systems, not only in terms of guaranteed outer bounds but also in terms of an inner enclosure that belongs to the true solution set with certainty. Because previous work has focused on the definition and computationally efficient implementation of arithmetic operations and extensions of nonlinear standard functions, where all arguments are replaced by thick ellipsoids, this paper introduces novel operators for specifically evaluating quasi-linear system models with bounded parameters as well as for the union and intersection of thick ellipsoids. These techniques are combined in such a way that a discrete-time state observer can be designed in a predictor-corrector framework. Estimation results are presented for a combined observer-based estimation of state variables as well as disturbance forces and torques in the sense of an unknown input estimator for a hovercraft. View Full-Text
Keywords: set-valued state estimation; ellipsoidal enclosures; outer state enclosures; inner enclosures; set-valued intersection and union; thick ellipsoids set-valued state estimation; ellipsoidal enclosures; outer state enclosures; inner enclosures; set-valued intersection and union; thick ellipsoids
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MDPI and ACS Style

Rauh, A.; Bourgois, A.; Jaulin, L. Union and Intersection Operators for Thick Ellipsoid State Enclosures: Application to Bounded-Error Discrete-Time State Observer Design. Algorithms 2021, 14, 88. https://doi.org/10.3390/a14030088

AMA Style

Rauh A, Bourgois A, Jaulin L. Union and Intersection Operators for Thick Ellipsoid State Enclosures: Application to Bounded-Error Discrete-Time State Observer Design. Algorithms. 2021; 14(3):88. https://doi.org/10.3390/a14030088

Chicago/Turabian Style

Rauh, Andreas, Auguste Bourgois, and Luc Jaulin. 2021. "Union and Intersection Operators for Thick Ellipsoid State Enclosures: Application to Bounded-Error Discrete-Time State Observer Design" Algorithms 14, no. 3: 88. https://doi.org/10.3390/a14030088

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