×

zbMATH — the first resource for mathematics

Convergence analysis of a mixed controlled \(l_{2} - l_{p}\) adaptive algorithm. (English) Zbl 1204.93115
Summary: A newly developed adaptive scheme for system identification is proposed. The proposed algorithm is a mixture of two norms, namely, the \(l_2\)-norm and the \(l_p\)-norm (\(p\geq 1\)), where a controlling parameter in the range \([0,1]\) is used to control the mixture of the two norms. Existing algorithms based on mixed norm can be considered as a special case of the proposed algorithm. Therefore, our algorithm can be seen as a generalization to these algorithms. The derivation of the algorithm and its convexity property are reported and detailed. Also, the first moment behaviour as well as the second moment behaviour of the weights is studied. Bounds for the step size on the convergence of the proposed algorithm are derived, and the steady-state analysis is carried out. Finally, simulation results are performed and are found to corroborate with the theory developed.

MSC:
93E10 Estimation and detection in stochastic control theory
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] doi:10.1109/TIT.1958.1057451 · doi:10.1109/TIT.1958.1057451
[2] doi:10.1109/TCS.1981.1085011 · doi:10.1109/TCS.1981.1085011
[3] doi:10.1109/TIT.1984.1056890 · Zbl 0547.93064 · doi:10.1109/TIT.1984.1056890
[4] doi:10.1109/TASSP.1985.1164493 · doi:10.1109/TASSP.1985.1164493
[5] doi:10.1109/TASSP.1987.1165197 · doi:10.1109/TASSP.1987.1165197
[6] doi:10.1109/18.133267 · Zbl 0754.93072 · doi:10.1109/18.133267
[7] doi:10.1109/78.286951 · doi:10.1109/78.286951
[8] doi:10.1049/el:19991080 · doi:10.1049/el:19991080
[9] doi:10.1049/ip-f-2.1993.0006 · doi:10.1049/ip-f-2.1993.0006
[10] doi:10.1109/TIT.1984.1056886 · doi:10.1109/TIT.1984.1056886
[11] doi:10.1049/ip-vis:19960449 · doi:10.1049/ip-vis:19960449
[12] doi:10.1049/el:19961202 · doi:10.1049/el:19961202
[13] doi:10.1109/78.575705 · doi:10.1109/78.575705
[14] doi:10.1049/ip-i-2.1990.0031 · doi:10.1049/ip-i-2.1990.0031
[15] doi:10.1109/TIT.1958.1057444 · doi:10.1109/TIT.1958.1057444
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.