The Experts below are selected from a list of 15789 Experts worldwide ranked by ideXlab platform
Yaojie Mi - One of the best experts on this subject based on the ideXlab platform.
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Tension identification of two-motor system based on neural network Left-Inverse
2014 International Joint Conference on Neural Networks (IJCNN), 2014Co-Authors: Wenxiang Zhao, Hao Zhang, Yan Jiang, Yaojie MiAbstract:Tension detection is a key to improve performance of two-motor system under sensorless operation. This paper presents a new identification method for two-motor system based on artificial neural network and the Left-Inverse theory. Considering that the system parameters are time-variant and the mathematic model of Left-Inverse identification is complex, BP neural network is used to build the Left-Inverse model in this method, which is easy to implement. A simulation model of a two-motor system is developed. The simulated results verify the proposed method. By using this control strategy, the tension can be identified quickly and accurately, in which satisfactory robustness is offered.
Yuri Luchko - One of the best experts on this subject based on the ideXlab platform.
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fractional derivatives and the fundamental theorem of fractional calculus
Fractional Calculus and Applied Analysis, 2020Co-Authors: Yuri LuchkoAbstract:In this paper, we address the one-parameter families of the fractional integrals and derivatives defined on a finite interval. First we remind the reader of the known fact that under some reasonable conditions, there exists precisely one unique family of the fractional integrals, namely, the well-known Riemann-Liouville fractional integrals. As to the fractional derivatives, their natural definition follows from the fundamental theorem of the Fractional Calculus, i.e., they are introduced as the Left-Inverse operators to the Riemann-Liouville fractional integrals. Until now, three families of such derivatives were suggested in the literature: the Riemann-Liouville fractional derivatives, the Caputo fractional derivatives, and the Hilfer fractional derivatives. We clarify the interconnections between these derivatives on different spaces of functions and provide some of their properties including the formulas for their projectors and the Laplace transforms. However, it turns out that there exist infinitely many other families of the fractional derivatives that are the Left-Inverse operators to the Riemann-Liouville fractional integrals. In this paper, we focus on an important class of these fractional derivatives and discuss some of their properties.
Wenxiang Zhao - One of the best experts on this subject based on the ideXlab platform.
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Tension identification of two-motor system based on neural network Left-Inverse
2014 International Joint Conference on Neural Networks (IJCNN), 2014Co-Authors: Wenxiang Zhao, Hao Zhang, Yan Jiang, Yaojie MiAbstract:Tension detection is a key to improve performance of two-motor system under sensorless operation. This paper presents a new identification method for two-motor system based on artificial neural network and the Left-Inverse theory. Considering that the system parameters are time-variant and the mathematic model of Left-Inverse identification is complex, BP neural network is used to build the Left-Inverse model in this method, which is easy to implement. A simulation model of a two-motor system is developed. The simulated results verify the proposed method. By using this control strategy, the tension can be identified quickly and accurately, in which satisfactory robustness is offered.
Radu Balan - One of the best experts on this subject based on the ideXlab platform.
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on lipschitz analysis and lipschitz synthesis for the phase retrieval problem
Linear Algebra and its Applications, 2016Co-Authors: Radu BalanAbstract:Abstract We prove two results with regard to reconstruction from magnitudes of frame coefficients (the so called “phase retrieval problem”). First we show that phase retrievable nonlinear maps are bi-Lipschitz with respect to appropriate metrics on the quotient space. Specifically, if nonlinear analysis maps α , β : H ˆ → R m are injective, with α ( x ) = ( | 〈 x , f k 〉 | ) k = 1 m and β ( x ) = ( | 〈 x , f k 〉 | 2 ) k = 1 m , where { f 1 , … , f m } is a frame for a Hilbert space H and H ˆ = H / T 1 , then α is bi-Lipschitz with respect to the class of “natural metrics” D p ( x , y ) = min φ ‖ x − e i φ y ‖ p , whereas β is bi-Lipschitz with respect to the class of matrix-norm induced metrics d p ( x , y ) = ‖ x x ⁎ − y y ⁎ ‖ p . Second we prove that reconstruction can be performed using Lipschitz continuous maps. That is, there exist Left Inverse maps (synthesis maps) ω , ψ : R m → H ˆ of α and β respectively, that are Lipschitz continuous with respect to appropriate metrics. Additionally, we obtain the Lipschitz constants of ω and ψ in terms of the lower Lipschitz constants of α and β , respectively. Surprisingly, the increase in both Lipschitz constants is a relatively small factor, independent of the space dimension or the frame redundancy.
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on lipschitz analysis and lipschitz synthesis for the phase retrieval problem
arXiv: Functional Analysis, 2015Co-Authors: Radu BalanAbstract:In this paper we prove two results regarding reconstruction from magnitudes of frame coefficients (the so called "phase retrieval problem"). First we show that phase retrievability as an algebraic property implies that nonlinear maps are bi-Lipschitz with respect to appropriate metrics on the quotient space. Second we prove that reconstruction can be performed using Lipschitz continuous maps. Specifically we show that when nonlinear analysis maps $\alpha,\beta:\hat{H}\rightarrow R^m$ are injective, with $\alpha(x)=(|\langle x,f_k\rangle |)_{k=1}^m$ and $\beta(x)=(|\langle x,f_k \rangle|^2)_{k=1}^m$, where $\{f_1,\ldots,f_m\}$ is a frame for a Hilbert space $H$ and $\hat{H}=H/T^1$, then $\alpha$ is bi-Lipschitz with respect to the class of "natural metrics" $D_p(x,y)= min_{\varphi} || x-e^{i\varphi}y {||}_p$, whereas $\beta$ is bi-Lipschitz with respect to the class of matrix-norm induced metrics $d_p(x,y)=|| xx^*-yy^*{||}_p$. Furthermore, there exist Left Inverse maps $\omega,\psi:R^m\rightarrow \hat{H}$ of $\alpha$ and $\beta$ respectively, that are Lipschitz continuous with respect to the appropriate metric. Additionally we obtain the Lipschitz constants of these Inverse maps in terms of the lower Lipschitz constants of $\alpha$ and $\beta$. Surprisingly the increase in Lipschitz constant is a relatively small factor, independent of the space dimension or the frame redundancy.
Hao Zhang - One of the best experts on this subject based on the ideXlab platform.
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Tension identification of two-motor system based on neural network Left-Inverse
2014 International Joint Conference on Neural Networks (IJCNN), 2014Co-Authors: Wenxiang Zhao, Hao Zhang, Yan Jiang, Yaojie MiAbstract:Tension detection is a key to improve performance of two-motor system under sensorless operation. This paper presents a new identification method for two-motor system based on artificial neural network and the Left-Inverse theory. Considering that the system parameters are time-variant and the mathematic model of Left-Inverse identification is complex, BP neural network is used to build the Left-Inverse model in this method, which is easy to implement. A simulation model of a two-motor system is developed. The simulated results verify the proposed method. By using this control strategy, the tension can be identified quickly and accurately, in which satisfactory robustness is offered.