Displaying similar documents to “Recursive set membership estimation for output-error fractional models with unknown-but-bounded errors”

Normalized finite fractional differences: Computational and accuracy breakthroughs

Rafał Stanisławski, Krzysztof J. Latawiec (2012)

International Journal of Applied Mathematics and Computer Science

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This paper presents a series of new results in finite and infinite-memory modeling of discrete-time fractional differences. The introduced normalized finite fractional difference is shown to properly approximate its fractional difference original, in particular in terms of the steady-state properties. A stability analysis is also presented and a recursive computation algorithm is offered for finite fractional differences. A thorough analysis of computational and accuracy aspects is culminated...

Fractional-order Bessel functions with various applications

Haniye Dehestani, Yadollah Ordokhani, Mohsen Razzaghi (2019)

Applications of Mathematics

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We introduce fractional-order Bessel functions (FBFs) to obtain an approximate solution for various kinds of differential equations. Our main aim is to consider the new functions based on Bessel polynomials to the fractional calculus. To calculate derivatives and integrals, we use Caputo fractional derivatives and Riemann-Liouville fractional integral definitions. Then, operational matrices of fractional-order derivatives and integration for FBFs are derived. Also, we discuss an error...

Fractional kalman filter algorithm for the states parameters and order of fractional system estimation

Dominik Sierociuk, Andrzej Dzieliński (2006)

International Journal of Applied Mathematics and Computer Science

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This paper presents a generalization of the Kalman filter for linear and nonlinear fractional order discrete state-space systems. Linear and nonlinear discrete fractional order state-space systems are also introduced. The simplified kalman filter for the linear case is called the fractional Kalman filter and its nonlinear extension is named the extended fractional Kalman filter. The background and motivations for using such techniques are given, and some algorithms are discussed. The...

Design of unknown input fractional-order observers for fractional-order systems

Ibrahima N'Doye, Mohamed Darouach, Holger Voos, Michel Zasadzinski (2013)

International Journal of Applied Mathematics and Computer Science

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This paper considers a method of designing fractional-order observers for continuous-time linear fractional-order systems with unknown inputs. Conditions for the existence of these observers are given. Sufficient conditions for the asymptotical stability of fractional-order observer errors with the fractional order α satisfying 0 < α < 2 are derived in terms of linear matrix inequalities. Two numerical examples are given to demonstrate the applicability of the proposed approach,...

Weak solvability and numerical analysis of a class of time-fractional hemivariational inequalities with application to frictional contact problems

Mustapha Bouallala (2024)

Applications of Mathematics

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We investigate a generalized class of fractional hemivariational inequalities involving the time-fractional aspect. The existence result is established by employing the Rothe method in conjunction with the surjectivity of multivalued pseudomonotone operators and the properties of the Clarke generalized gradient. We are also exploring a numerical approach to address the problem, utilizing both spatially semi-discrete and fully discrete finite elements, along with a discrete approximation...

Certified metamodels for sensitivity indices estimation

Alexandre Janon, Maëlle Nodet, Clémentine Prieur (2012)

ESAIM: Proceedings

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Global sensitivity analysis of a numerical code, more specifically estimation of Sobol indices associated with input variables, generally requires a large number of model runs. When those demand too much computation time, it is necessary to use a reduced model (metamodel) to perform sensitivity analysis, whose outputs are numerically close to the ones of the original model, while being much faster to run. In this case, estimated indices are subject to two kinds of errors: sampling error,...

A comparison of some a posteriori error estimates for fourth order problems

Segeth, Karel

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A lot of papers and books analyze analytical a posteriori error estimates from the point of view of robustness, guaranteed upper bounds, global efficiency, etc. At the same time, adaptive finite element methods have acquired the principal position among algorithms for solving differential problems in many physical and technical applications. In this survey contribution, we present and compare, from the viewpoint of adaptive computation, several recently published error estimation procedures...