An improved LMS algorithm based on fractional order gradient direction

This paper mainly focuses on the LMS algorithm based on fractional order gradient information, which extends the first order gradient of traditional LMS algorithm to fractional order a (0 < a ≤ 1). Since the LMS algorithm generally does not converge to the true extreme value point of the objectiv...

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Bibliographic Details
Published inChinese Control Conference pp. 3156 - 3161
Main Authors Zhang, Haozhe, Mo, Lipo
Format Conference Proceeding
LanguageEnglish
Published Technical Committee on Control Theory, Chinese Association of Automation 25.07.2022
Subjects
Convergence
Convergence speed
Fractional order calculus
Fractional order gradient
Lead
Linear programming
LMS algorithm
Mathematical analysis
Steady-state
Truncating
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ISSN1934-1768
DOI10.23919/CCC55666.2022.9902725

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Summary:This paper mainly focuses on the LMS algorithm based on fractional order gradient information, which extends the first order gradient of traditional LMS algorithm to fractional order a (0 < a ≤ 1). Since the LMS algorithm generally does not converge to the true extreme value point of the objective function when fractional order gradient is used. To ensure convergence, the strategy of truncating the second order term of the fractional order gradient expansion of the objective function is adopted. The step size condition for convergence is given and the performance of the algorithm with different fractional orders a is analyzed. It is shown that under certain conditions, a larger fractional order a will lead a faster convergence speed. Finally, the effectiveness of the proposed algorithm is illustrated by four simulation examples.
ISSN:1934-1768
DOI:10.23919/CCC55666.2022.9902725