Boundedness and continuity of maximal singular integrals and maximal functions on Triebel-Lizorkin spaces

Liu, Feng; Xue, Qingying; KôzôYabuta,

doi:10.1007/s11425-017-9416-5

Cited by 9 publications

(10 citation statements)

References 30 publications

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“…• The simulation results indicate that the proposed algorithms are effective for estimating the parameters of stochastic systems. • The proposed methods in this paper can be extended to model industrial processes and network systems [79][80][81][82][83][84] by means of some other mathematical tools and approaches [85][86][87][88][89][90].…”

Section: Discussionmentioning

confidence: 99%

Gradient-Based Iterative Parameter Estimation Algorithms for Dynamical Systems from Observation Data

et al. 2019

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It is well-known that mathematical models are the basis for system analysis and controller design. This paper considers the parameter identification problems of stochastic systems by the controlled autoregressive model. A gradient-based iterative algorithm is derived from observation data by using the gradient search. By using the multi-innovation identification theory, we propose a multi-innovation gradient-based iterative algorithm to improve the performance of the algorithm. Finally, a numerical simulation example is given to demonstrate the effectiveness of the proposed algorithms.

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Section: Discussionmentioning

confidence: 99%

Gradient-Based Iterative Parameter Estimation Algorithms for Dynamical Systems from Observation Data

et al. 2019

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“…The analysis and numerical example indicate that the PC-RGELS algorithm can give more accurate parameter estimates than the RGELS algorithm. Furthermore, the proposed methods can be extended to other fields by means of some other mathematical tools and approaches [80][81][82][83][84][85][86] to model industrial processes [87][88][89][90][91][92][93][94][95][96][97][98].…”

Section: Discussionmentioning

confidence: 99%

Recursive Algorithms for Multivariable Output-Error-Like ARMA Systems

Pan

et al. 2019

Mathematics

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This paper studies the parameter identification problems for multivariable output-error-like systems with colored noises. Based on the hierarchical identification principle, the original system is decomposed into several subsystems. However, each subsystem contains the same parameter vector, which leads to redundant computation. By taking the average of the parameter estimation vectors of each subsystem, a partially-coupled subsystem recursive generalized extended least squares (PC-S-RGELS) algorithm is presented to cut down the redundant parameter estimates. Furthermore, a partially-coupled recursive generalized extended least squares (PC-RGELS) algorithm is presented to further reduce the computational cost and the redundant estimates by using the coupling identification concept. Finally, an example indicates the effectiveness of the derived algorithms.

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“…Compared with the least-squares-based iterative identification algorithm, the proposed algorithms achieve highly accurate parameter estimates and improve the performance the algorithms. The proposed decomposition least-squares-based iterative identification algorithms for multivariable equation-error autoregressive moving average systems can combine other estimation methods [71][72][73][74] and the mathematical techniques [75][76][77] to explore the parameter identification methods of other scalar, multivariable linear, nonlinear systems with colored noises [78][79][80], and can be extended to other scientific fields [81][82][83][84][85][86][87][88] such as signal modeling and communication networked systems [89][90][91][92].…”

Section: Discussionmentioning

confidence: 99%

Decomposition Least-Squares-Based Iterative Identification Algorithms for Multivariable Equation-Error Autoregressive Moving Average Systems

et al. 2019

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This paper is concerned with the identification problem for multivariable equation-error systems whose disturbance is an autoregressive moving average process. By means of the hierarchical identification principle and the iterative search, a hierarchical least-squares-based iterative (HLSI) identification algorithm is derived and a least-squares-based iterative (LSI) identification algorithm is given for comparison. Furthermore, a hierarchical multi-innovation least-squares-based iterative (HMILSI) identification algorithm is proposed using the multi-innovation theory. Compared with the LSI algorithm, the HLSI algorithm has smaller computational burden and can give more accurate parameter estimates and the HMILSI algorithm can track time-varying parameters. Finally, a simulation example is provided to verify the effectiveness of the proposed algorithms.

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Boundedness and continuity of maximal singular integrals and maximal functions on Triebel-Lizorkin spaces

Cited by 9 publications

References 30 publications

Gradient-Based Iterative Parameter Estimation Algorithms for Dynamical Systems from Observation Data

Gradient-Based Iterative Parameter Estimation Algorithms for Dynamical Systems from Observation Data

Recursive Algorithms for Multivariable Output-Error-Like ARMA Systems

Decomposition Least-Squares-Based Iterative Identification Algorithms for Multivariable Equation-Error Autoregressive Moving Average Systems

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