Differentiation similarities in fractional pseudo-state space representations and the subspace-based methods

Malti, Rachid; Thomassin, Magalie

doi:10.2478/s13540-013-0017-8

Cited by 12 publications

(5 citation statements)

References 24 publications

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“…That's why the results of the paper are limited to the case when 0 < ν < 1. However, when 1 < ν < 2, differentiation similarity transformation can be applied [35] and an equivalent system of dimension 2n can be obtained with a commensurate order equal to ν 2 .…”

Section: Synthesis Of Fractional Interval Observersmentioning

confidence: 99%

Fractional interval observers and initialization of fractional systems

Frej

Malti

Aoun

et al. 2020

Communications in Nonlinear Science and Numerical Simulation

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In this paper an interval observer is synthesized for fractional linear systems with additive noise and disturbances. The contribution of system whole past to future output is taken into account as an initialization function. Provided the initialization function is upper and lower bounded, it is shown in this paper that the fractional interval observer (FIO) allows to bound pseudo-state free responses by an upper and a lower trajectory. In case interval observers cannot be synthesized straightforwardly, so as to obtain a stable and non-negative estimation error, it is shown that a change of coordinates allows to overcome this problem. The proposed methodology allows to bound fractional systems trajectories when the whole past is unknown but can be bounded. Finally, a numerical example is given to show the effectiveness of the proposed methods on the initialization of fractional linear systems.

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Section: Synthesis Of Fractional Interval Observersmentioning

confidence: 99%

Fractional interval observers and initialization of fractional systems

Frej

Malti

Aoun

et al. 2020

Communications in Nonlinear Science and Numerical Simulation

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“…Stacking (2b) and all its α-order derivatives into a column vector, the input-output relationship can be written as [22]…”

Section: A Constructing Massive Mimo Data Matrices For Channel Identmentioning

confidence: 99%

Fractional-Order System Identification and Equalization in Massive MIMO Systems

Lupupa

Hadjiloucas

2020

IEEE Access

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In this paper, a new methodology for the identification and equalization of massive Multiple-Input Multiple-Output (MIMO) channels in fifth generation (5G) wireless communications is proposed. Channel equalization is performed in state-space, having estimated the channel using the fractional-order Multivariable Output Error State Space (MOESP) system identification algorithm. The proposed fractional-order algorithm is an improvement over its integer-order counterpart that is currently used for state-space channel identification/ estimation and state-space channel equalization. When dealing with fractional-order calculus our work adopts the Riemann-Liouville definition. Our numerical results of channel identification having used a chirp signal to excite our massive MIMO system show a lower mean square error (MSE) in channel estimation using the proposed fractional-order MOESP identification algorithm when compared to integer-order MOESP identification algorithm of increased order. Furthermore, following equalization, transmission using Binary phase shift keying (BPSK), Quadrature phase shift keying (QPSK) and 256-Quadrature amplitude modulation (256-QAM) signals show that the symbol error rate (SER) as a function of signal to noise ratio (SNR) performance of the fractional-order equalization algorithm compares to that of the integer-order equalization algorithm. The proposed channel identification algorithm also provides a more parsimonious solution for modelling multipath fading, thus enabling the design of fractional-order equalizers. In addition, they may be used in other applications where high order filtering and more complex control algorithms which are difficult to tune would be needed. Finally, the work has other technological applications where there is a requirement for modelling and control of propagation processes in dispersive media.

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“…It has been further shown in [32] that if (1)-(2) is observable (similarly controllable), then (3)-(4) is also observable (similarly controllable).…”

Section: B Differentiation Similarity Transformationsmentioning

confidence: 99%

“…Subspace-based methods for system identification using fractional models are developed in the time-domain in the deterministic context in [30] and the stochastic context in [31] and [32]. So, the proposed method inherits the advantages of subspace methods which stem from the reliability of numerical algorithms using the QR and the singular value decomposition [33].…”

Section: Introductionmentioning

confidence: 99%

“…It is shown in this paper, that an overestimated pseudo-state-space representation might have multiple global minimums. For that purpose, a new concept of differentiation similarity transformations for commensurate pseudo-states-space representations is introduced in [32]. It proves that a pseudo-state-space representation with a commensurate differentiation order ν and a dimension of the transition matrix N can be similar to a pseudo-statespace representation with a commensurate order ν/k and a dimension of the transition matrix kN , where k is an integral number.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Frequency-domain subspace system identification with fractional differentiation models

Иванова¹,

Malti²,

Moreau³

2014

2014 IEEE/ASME 10th International Conference on Mechatronic and Embedded Systems and Applications (MESA)

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In this paper, an algorithm based on subspace method from the MOESP (MIMO Ouput-Erreur State sPace) family is presented, for state-space identification of continuoustime fractional commensurate models, using samples of frequency data. As compared to the rational state-space representation, the commensurate differentiation order must be estimated besides the state-space matrices, estimated with conventional subspacebased techniques using QR and singular value decomposition. This is the first method developed for multi-input multi-output system identification of fractional models in the frequency domain.

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Differentiation similarities in fractional pseudo-state space representations and the subspace-based methods

Cited by 12 publications

References 24 publications

Fractional interval observers and initialization of fractional systems

Fractional interval observers and initialization of fractional systems

Fractional-Order System Identification and Equalization in Massive MIMO Systems

Frequency-domain subspace system identification with fractional differentiation models

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