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J. Control</a> <a href="/?q=in%3A288552" title="Articles in this Issue">84, No. 7, 1275-1294 (2011)</a>. </div> <div class="abstract">Summary: In this article we review the recent advances in Iterative Learning Control (ILC) for nonlinear dynamic systems. In the research field of ILC, two categories of system nonlinearities are considered, namely, the Global Lipschitz Continuous (GLC) functions and Local Lipschitz Continuous (LLC) functions. ILC for GLC systems is widely studied and analyzed using contraction mapping approach, and the focus of recent exploration moves to application problems, though a number of theoretical issues remain open. ILC for LLC systems is currently a hot area and the recent research focuses on ILC design and analysis by means of Lyapunov&rsquo;s approach. The objectives of this article are to introduce recent development and advances in nonlinear ILC schemes, highlight their effectiveness and limitations, as well as to discuss the directions for further exploration of nonlinear ILC.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A5973411">Cited in <strong>107</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A93C10" title="MSC2020">93C10</a> </td> <td class="space"> Nonlinear systems in control theory </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A68T05" title="MSC2020">68T05</a> </td> <td class="space"> Learning and adaptive systems in artificial intelligence </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93-02" title="MSC2020">93-02</a> </td> <td class="space"> Research exposition (monographs, survey articles) pertaining to systems and control theory </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aiterative+learning+control">iterative learning control</a>; <a href="/?q=ut%3Anonlinear+systems">nonlinear systems</a>; <a href="/?q=ut%3Asurvey">survey</a>; <a href="/?q=ut%3Aglobal+Lipschitz+continuous+functions">global Lipschitz continuous functions</a>; <a href="/?q=ut%3Alocal+Lipschitz+continuous+functions">local Lipschitz continuous functions</a></div> <!-- Modal used to show zbmath metadata in different output formats--> <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">&times;</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;"> <!-- alert for connection errors etc --> </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function"> <!-- Button trigger metadata modal --> <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1227.93053" data-ciurl="/ci/05973411" data-biburl="/bibtex/05973411.bib" data-amsurl="/amsrefs/05973411.bib" data-xmlurl="/xml/05973411.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/05973411.pdf" title="Zbl 1227.93053 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1080/00207179.2011.574236" aria-label="DOI for “A survey on iterative learning control for nonlinear systems”" title="10.1080/00207179.2011.574236">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Ahn, HS and Chen, YQ. 2009. Iterative Learning Control for Multi-agent Formation. Proceedings of ICROS-SICE International Joint Conference. 2009. pp.3111&ndash;3116. Gwangju, South Korea</td> </tr><tr> <td>[2]</td> <td class="space">DOI: 10.1109/TMAG.2004.840182&nbsp;&middot; <a href="https://doi.org/10.1109/TMAG.2004.840182" class="nowrap">doi:10.1109/TMAG.2004.840182</a></td> </tr><tr> <td>[3]</td> <td class="space">Ahn HS, Iterative Learning Control: Robustness and Monotonic Convergence in the Iteration Domain, Communications and Control Engineering Series (2007)</td> </tr><tr> <td>[4]</td> <td class="space">DOI: 10.1002/rob.4620010203&nbsp;&middot; <a href="https://doi.org/10.1002/rob.4620010203" class="nowrap">doi:10.1002/rob.4620010203</a></td> </tr><tr> <td>[5]</td> <td class="space">Aström KL, Computer-controlled Systems &ndash; Theory and Design (1997)</td> </tr><tr> <td>[6]</td> <td class="space">DOI: 10.1049/ip-d.1989.0016 &middot; <a href="/0731.93047" class="nowrap">Zbl 0731.93047</a>&nbsp;&middot; <a href="https://doi.org/10.1049/ip-d.1989.0016" class="nowrap">doi:10.1049/ip-d.1989.0016</a></td> </tr><tr> <td>[7]</td> <td class="space">DOI: 10.1007/978-1-4615-5629-9&nbsp;&middot; <a href="https://doi.org/10.1007/978-1-4615-5629-9" class="nowrap">doi:10.1007/978-1-4615-5629-9</a></td> </tr><tr> <td>[8]</td> <td class="space">DOI: 10.1109/TAC.2007.914252 &middot; <a href="/1367.93736" class="nowrap">Zbl 1367.93736</a>&nbsp;&middot; <a href="https://doi.org/10.1109/TAC.2007.914252" class="nowrap">doi:10.1109/TAC.2007.914252</a></td> </tr><tr> <td>[9]</td> <td class="space">DOI: 10.1109/MCS.2006.1636313&nbsp;&middot; <a href="https://doi.org/10.1109/MCS.2006.1636313" class="nowrap">doi:10.1109/MCS.2006.1636313</a></td> </tr><tr> <td>[10]</td> <td class="space">DOI: 10.1016/S0005-1098(97)00196-9 &middot; <a href="/0912.93031" class="nowrap">Zbl 0912.93031</a>&nbsp;&middot; <a href="https://doi.org/10.1016/S0005-1098(97)00196-9" class="nowrap">doi:10.1016/S0005-1098(97)00196-9</a></td> </tr><tr> <td>[11]</td> <td class="space">Chen YQ, Iterative Learning Control: Convergence, Robustness and Applications, Lecture Notes Series on Control and Information Science, Vol. 248 248 (1999)</td> </tr><tr> <td>[12]</td> <td class="space">DOI: 10.1109/9.746269 &middot; <a href="/1056.93646" class="nowrap">Zbl 1056.93646</a>&nbsp;&middot; <a href="https://doi.org/10.1109/9.746269" class="nowrap">doi:10.1109/9.746269</a></td> </tr><tr> <td>[13]</td> <td class="space">DOI: 10.1080/002071797223640 &middot; <a href="/0886.93036" class="nowrap">Zbl 0886.93036</a>&nbsp;&middot; <a href="https://doi.org/10.1080/002071797223640" class="nowrap">doi:10.1080/002071797223640</a></td> </tr><tr> <td>[14]</td> <td class="space">DOI: 10.1016/j.automatica.2007.12.004 &middot; <a href="/1283.93329" class="nowrap">Zbl 1283.93329</a>&nbsp;&middot; <a href="https://doi.org/10.1016/j.automatica.2007.12.004" class="nowrap">doi:10.1016/j.automatica.2007.12.004</a></td> </tr><tr> <td>[15]</td> <td class="space">Chi RH, Hou, Z.S., and Xu, J.-X. (2010)</td> </tr><tr> <td>[16]</td> <td class="space">DOI: 10.1109/TFUZZ.2007.902021&nbsp;&middot; <a href="https://doi.org/10.1109/TFUZZ.2007.902021" class="nowrap">doi:10.1109/TFUZZ.2007.902021</a></td> </tr><tr> <td>[17]</td> <td class="space">DOI: 10.1080/002071700405824 &middot; <a href="/1006.93596" class="nowrap">Zbl 1006.93596</a>&nbsp;&middot; <a href="https://doi.org/10.1080/002071700405824" class="nowrap">doi:10.1080/002071700405824</a></td> </tr><tr> <td>[18]</td> <td class="space">DOI: 10.1016/0893-6080(89)90003-8&nbsp;&middot; <a href="https://doi.org/10.1016/0893-6080(89)90003-8" class="nowrap">doi:10.1016/0893-6080(89)90003-8</a></td> </tr><tr> <td>[19]</td> <td class="space">Goodwin GC, Adaptive Filtering Prediction and Control (1984)</td> </tr><tr> <td>[20]</td> <td class="space">DOI: 10.1109/9.109644&nbsp;&middot; <a href="https://doi.org/10.1109/9.109644" class="nowrap">doi:10.1109/9.109644</a></td> </tr><tr> <td>[21]</td> <td class="space">DOI: 10.1137/1.9780898718683 &middot; <a href="/1087.93003" class="nowrap">Zbl 1087.93003</a>&nbsp;&middot; <a href="https://doi.org/10.1137/1.9780898718683" class="nowrap">doi:10.1137/1.9780898718683</a></td> </tr><tr> <td>[22]</td> <td class="space">DOI: 10.1016/j.automatica.2006.02.001 &middot; <a href="/1116.93405" class="nowrap">Zbl 1116.93405</a>&nbsp;&middot; <a href="https://doi.org/10.1016/j.automatica.2006.02.001" class="nowrap">doi:10.1016/j.automatica.2006.02.001</a></td> </tr><tr> <td>[23]</td> <td class="space">DOI: 10.1109/9.333794 &middot; <a href="/0825.93422" class="nowrap">Zbl 0825.93422</a>&nbsp;&middot; <a href="https://doi.org/10.1109/9.333794" class="nowrap">doi:10.1109/9.333794</a></td> </tr><tr> <td>[24]</td> <td class="space">Kawamura S, Proceedings of IEEE Symposium on Intelligent Control pp 365&ndash; (1987)</td> </tr><tr> <td>[25]</td> <td class="space">DOI: 10.1109/37.165507&nbsp;&middot; <a href="https://doi.org/10.1109/37.165507" class="nowrap">doi:10.1109/37.165507</a></td> </tr><tr> <td>[26]</td> <td class="space">DOI: 10.1049/ip-b.1980.0034&nbsp;&middot; <a href="https://doi.org/10.1049/ip-b.1980.0034" class="nowrap">doi:10.1049/ip-b.1980.0034</a></td> </tr><tr> <td>[27]</td> <td class="space">DOI: 10.1080/00207179608921632 &middot; <a href="/0850.93275" class="nowrap">Zbl 0850.93275</a>&nbsp;&middot; <a href="https://doi.org/10.1080/00207179608921632" class="nowrap">doi:10.1080/00207179608921632</a></td> </tr><tr> <td>[28]</td> <td class="space">Liu, CP, Xu, JX and Wu, J. 2009a. Iterative Learning Control with High-order Internal Model for Linear Time-varying Systems. Proceedings of IEEE American Control Conference. 2009a. pp.1634&ndash;1639. St Louis, MO</td> </tr><tr> <td>[29]</td> <td class="space">Liu, CP, Xu, J-X and Wu, J. 2009b. Iterative Learning Control for Network Systems with Communication Delay or Data Dropout. Proceedings of the 48th IEEE Conference on Decision and Control. 2009b. Shanghai.</td> </tr><tr> <td>[30]</td> <td class="space">DOI: 10.1002/acs.1163 &middot; <a href="/1204.93136" class="nowrap">Zbl 1204.93136</a>&nbsp;&middot; <a href="https://doi.org/10.1002/acs.1163" class="nowrap">doi:10.1002/acs.1163</a></td> </tr><tr> <td>[31]</td> <td class="space">DOI: 10.1109/TAC.2007.900827 &middot; <a href="/1366.93719" class="nowrap">Zbl 1366.93719</a>&nbsp;&middot; <a href="https://doi.org/10.1109/TAC.2007.900827" class="nowrap">doi:10.1109/TAC.2007.900827</a></td> </tr><tr> <td>[32]</td> <td class="space">DOI: 10.1080/002071700405905 &middot; <a href="/1006.93598" class="nowrap">Zbl 1006.93598</a>&nbsp;&middot; <a href="https://doi.org/10.1080/002071700405905" class="nowrap">doi:10.1080/002071700405905</a></td> </tr><tr> <td>[33]</td> <td class="space">Mallat SG, Transactions of the American Mathematical Society 315 pp 69&ndash; (1989)</td> </tr><tr> <td>[34]</td> <td class="space">DOI: 10.1109/TCSI.2008.2010103&nbsp;&middot; <a href="https://doi.org/10.1109/TCSI.2008.2010103" class="nowrap">doi:10.1109/TCSI.2008.2010103</a></td> </tr><tr> <td>[35]</td> <td class="space">DOI: 10.1109/TCST.2002.804117&nbsp;&middot; <a href="https://doi.org/10.1109/TCST.2002.804117" class="nowrap">doi:10.1109/TCST.2002.804117</a></td> </tr><tr> <td>[36]</td> <td class="space">Moore KL, Iterative Learning Control for Deterministic Systems, Advances in Industrial Control 22 (1993)&nbsp;&middot; <a href="https://doi.org/10.1007/978-1-4471-1912-8" class="nowrap">doi:10.1007/978-1-4471-1912-8</a></td> </tr><tr> <td>[37]</td> <td class="space">DOI: 10.1080/002071700405914 &middot; <a href="/1006.93599" class="nowrap">Zbl 1006.93599</a>&nbsp;&middot; <a href="https://doi.org/10.1080/002071700405914" class="nowrap">doi:10.1080/002071700405914</a></td> </tr><tr> <td>[38]</td> <td class="space">DOI: 10.1002/rnc.1231 &middot; <a href="/1284.93104" class="nowrap">Zbl 1284.93104</a>&nbsp;&middot; <a href="https://doi.org/10.1002/rnc.1231" class="nowrap">doi:10.1002/rnc.1231</a></td> </tr><tr> <td>[39]</td> <td class="space">Moore, KL, Chen, YQ and Ahn, HS. 2006. Iterative Learning Control: A Tutorial and Big Picture View. Proceedings of 45th IEEE Conference of Decision and Control. 2006. pp.2352&ndash;2357.</td> </tr><tr> <td>[40]</td> <td class="space">DOI: 10.1080/002071700405798 &middot; <a href="/0996.00532" class="nowrap">Zbl 0996.00532</a>&nbsp;&middot; <a href="https://doi.org/10.1080/002071700405798" class="nowrap">doi:10.1080/002071700405798</a></td> </tr><tr> <td>[41]</td> <td class="space">Nguyen DH, Journal of system Control 19 pp 1054&ndash; (2009)</td> </tr><tr> <td>[42]</td> <td class="space">DOI: 10.1109/TRA.2002.999653&nbsp;&middot; <a href="https://doi.org/10.1109/TRA.2002.999653" class="nowrap">doi:10.1109/TRA.2002.999653</a></td> </tr><tr> <td>[43]</td> <td class="space">DOI: 10.1080/00207170210159122 &middot; <a href="/1030.93016" class="nowrap">Zbl 1030.93016</a>&nbsp;&middot; <a href="https://doi.org/10.1080/00207170210159122" class="nowrap">doi:10.1080/00207170210159122</a></td> </tr><tr> <td>[44]</td> <td class="space">DOI: 10.1016/0167-6911(83)90021-X &middot; <a href="/0524.93037" class="nowrap">Zbl 0524.93037</a>&nbsp;&middot; <a href="https://doi.org/10.1016/0167-6911(83)90021-X" class="nowrap">doi:10.1016/0167-6911(83)90021-X</a></td> </tr><tr> <td>[45]</td> <td class="space">DOI: 10.1080/00207170701579403 &middot; <a href="/1152.93515" class="nowrap">Zbl 1152.93515</a>&nbsp;&middot; <a href="https://doi.org/10.1080/00207170701579403" class="nowrap">doi:10.1080/00207170701579403</a></td> </tr><tr> <td>[46]</td> <td class="space">DOI: 10.1080/002071700405851 &middot; <a href="/1006.93601" class="nowrap">Zbl 1006.93601</a>&nbsp;&middot; <a href="https://doi.org/10.1080/002071700405851" class="nowrap">doi:10.1080/002071700405851</a></td> </tr><tr> <td>[47]</td> <td class="space">DOI: 10.1080/00207729108910607 &middot; <a href="/0722.93038" class="nowrap">Zbl 0722.93038</a>&nbsp;&middot; <a href="https://doi.org/10.1080/00207729108910607" class="nowrap">doi:10.1080/00207729108910607</a></td> </tr><tr> <td>[48]</td> <td class="space">Qu ZH, Robust Control of Nonlinear Uncertain Systems (1998)</td> </tr><tr> <td>[49]</td> <td class="space">DOI: 10.1111/j.1934-6093.2002.tb00336.x&nbsp;&middot; <a href="https://doi.org/10.1111/j.1934-6093.2002.tb00336.x" class="nowrap">doi:10.1111/j.1934-6093.2002.tb00336.x</a></td> </tr><tr> <td>[50]</td> <td class="space">Qu ZH, IEEE Transactions on Automatic Control 46 pp 1369&ndash; (2002) &middot; <a href="/1364.93889" class="nowrap">Zbl 1364.93889</a>&nbsp;&middot; <a href="https://doi.org/10.1109/TAC.2002.801194" class="nowrap">doi:10.1109/TAC.2002.801194</a></td> </tr><tr> <td>[51]</td> <td class="space">DOI: 10.1109/3477.604109&nbsp;&middot; <a href="https://doi.org/10.1109/3477.604109" class="nowrap">doi:10.1109/3477.604109</a></td> </tr><tr> <td>[52]</td> <td class="space">DOI: 10.1109/TEC.2004.832048&nbsp;&middot; <a href="https://doi.org/10.1109/TEC.2004.832048" class="nowrap">doi:10.1109/TEC.2004.832048</a></td> </tr><tr> <td>[53]</td> <td class="space">DOI: 10.1109/TPEL.2004.839807&nbsp;&middot; <a href="https://doi.org/10.1109/TPEL.2004.839807" class="nowrap">doi:10.1109/TPEL.2004.839807</a></td> </tr><tr> <td>[54]</td> <td class="space">DOI: 10.1109/72.165588&nbsp;&middot; <a href="https://doi.org/10.1109/72.165588" class="nowrap">doi:10.1109/72.165588</a></td> </tr><tr> <td>[55]</td> <td class="space">Slotine JJE, Applied Nonlinear Control (1991)</td> </tr><tr> <td>[56]</td> <td class="space">DOI: 10.1109/TAC.1987.1104616 &middot; <a href="/0611.93039" class="nowrap">Zbl 0611.93039</a>&nbsp;&middot; <a href="https://doi.org/10.1109/TAC.1987.1104616" class="nowrap">doi:10.1109/TAC.1987.1104616</a></td> </tr><tr> <td>[57]</td> <td class="space">DOI: 10.1016/S0005-1098(02)00003-1 &middot; <a href="/1002.93508" class="nowrap">Zbl 1002.93508</a>&nbsp;&middot; <a href="https://doi.org/10.1016/S0005-1098(02)00003-1" class="nowrap">doi:10.1016/S0005-1098(02)00003-1</a></td> </tr><tr> <td>[58]</td> <td class="space">Tan, Y and Xu, J-X. 2003. Learning Based Nonlinear Internal Model Control. Proceedings of IEEE 2003 American Control Conference. 2003. pp.3009&ndash;3013.</td> </tr><tr> <td>[59]</td> <td class="space">DOI: 10.1016/j.automatica.2004.01.026 &middot; <a href="/1051.93038" class="nowrap">Zbl 1051.93038</a>&nbsp;&middot; <a href="https://doi.org/10.1016/j.automatica.2004.01.026" class="nowrap">doi:10.1016/j.automatica.2004.01.026</a></td> </tr><tr> <td>[60]</td> <td class="space">DOI: 10.1109/TMECH.2008.2004627&nbsp;&middot; <a href="https://doi.org/10.1109/TMECH.2008.2004627" class="nowrap">doi:10.1109/TMECH.2008.2004627</a></td> </tr><tr> <td>[61]</td> <td class="space">DOI: 10.1109/TAC.2007.906215 &middot; <a href="/1366.93303" class="nowrap">Zbl 1366.93303</a>&nbsp;&middot; <a href="https://doi.org/10.1109/TAC.2007.906215" class="nowrap">doi:10.1109/TAC.2007.906215</a></td> </tr><tr> <td>[62]</td> <td class="space">Wang LX, Adaptive Fuzzy Systems and Control (1994)</td> </tr><tr> <td>[63]</td> <td class="space">DOI: 10.1016/j.jprocont.2007.10.014&nbsp;&middot; <a href="https://doi.org/10.1016/j.jprocont.2007.10.014" class="nowrap">doi:10.1016/j.jprocont.2007.10.014</a></td> </tr><tr> <td>[64]</td> <td class="space">DOI: 10.1016/S0005-1098(97)00140-4 &middot; <a href="/0907.93032" class="nowrap">Zbl 0907.93032</a>&nbsp;&middot; <a href="https://doi.org/10.1016/S0005-1098(97)00140-4" class="nowrap">doi:10.1016/S0005-1098(97)00140-4</a></td> </tr><tr> <td>[65]</td> <td class="space">DOI: 10.1109/9.661080 &middot; <a href="/0917.93054" class="nowrap">Zbl 0917.93054</a>&nbsp;&middot; <a href="https://doi.org/10.1109/9.661080" class="nowrap">doi:10.1109/9.661080</a></td> </tr><tr> <td>[66]</td> <td class="space">Xu J-X, Journal of Systems, Control and Information 45 pp 233&ndash; (2002)</td> </tr><tr> <td>[67]</td> <td class="space">DOI: 10.1016/S0005-1098(99)00100-4 &middot; <a href="/0939.93018" class="nowrap">Zbl 0939.93018</a>&nbsp;&middot; <a href="https://doi.org/10.1016/S0005-1098(99)00100-4" class="nowrap">doi:10.1016/S0005-1098(99)00100-4</a></td> </tr><tr> <td>[68]</td> <td class="space">DOI: 10.1016/S0005-1098(01)00049-8 &middot; <a href="/0987.93033" class="nowrap">Zbl 0987.93033</a>&nbsp;&middot; <a href="https://doi.org/10.1016/S0005-1098(01)00049-8" class="nowrap">doi:10.1016/S0005-1098(01)00049-8</a></td> </tr><tr> <td>[69]</td> <td class="space">DOI: 10.1109/TAC.2008.2007531 &middot; <a href="/1367.93325" class="nowrap">Zbl 1367.93325</a>&nbsp;&middot; <a href="https://doi.org/10.1109/TAC.2008.2007531" class="nowrap">doi:10.1109/TAC.2008.2007531</a></td> </tr><tr> <td>[70]</td> <td class="space">DOI: 10.1080/002071798222028 &middot; <a href="/0925.93714" class="nowrap">Zbl 0925.93714</a>&nbsp;&middot; <a href="https://doi.org/10.1080/002071798222028" class="nowrap">doi:10.1080/002071798222028</a></td> </tr><tr> <td>[71]</td> <td class="space">Xu J-X, Real-time Iterative Learning Control: Design and Applications, Advances in Industrial Control (2009)</td> </tr><tr> <td>[72]</td> <td class="space">DOI: 10.1016/S0005-1098(98)00036-3 &middot; <a href="/1040.93519" class="nowrap">Zbl 1040.93519</a>&nbsp;&middot; <a href="https://doi.org/10.1016/S0005-1098(98)00036-3" class="nowrap">doi:10.1016/S0005-1098(98)00036-3</a></td> </tr><tr> <td>[73]</td> <td class="space">DOI: 10.1016/S0005-1098(02)00021-3 &middot; <a href="/1013.93021" class="nowrap">Zbl 1013.93021</a>&nbsp;&middot; <a href="https://doi.org/10.1016/S0005-1098(02)00021-3" class="nowrap">doi:10.1016/S0005-1098(02)00021-3</a></td> </tr><tr> <td>[74]</td> <td class="space">DOI: 10.1109/TAC.2002.804460 &middot; <a href="/1364.93891" class="nowrap">Zbl 1364.93891</a>&nbsp;&middot; <a href="https://doi.org/10.1109/TAC.2002.804460" class="nowrap">doi:10.1109/TAC.2002.804460</a></td> </tr><tr> <td>[75]</td> <td class="space">Xu J-X, Linear and Nonlinear Iterative Learning Control, Lecture Notes in Control and Information Science, Vol. 291 (2003)</td> </tr><tr> <td>[76]</td> <td class="space">DOI: 10.1109/TNN.2006.886759&nbsp;&middot; <a href="https://doi.org/10.1109/TNN.2006.886759" class="nowrap">doi:10.1109/TNN.2006.886759</a></td> </tr><tr> <td>[77]</td> <td class="space">DOI: 10.1016/j.automatica.2004.01.029 &middot; <a href="/1077.93057" class="nowrap">Zbl 1077.93057</a>&nbsp;&middot; <a href="https://doi.org/10.1016/j.automatica.2004.01.029" class="nowrap">doi:10.1016/j.automatica.2004.01.029</a></td> </tr><tr> <td>[78]</td> <td class="space">DOI: 10.1109/TSMCB.2003.818433&nbsp;&middot; <a href="https://doi.org/10.1109/TSMCB.2003.818433" class="nowrap">doi:10.1109/TSMCB.2003.818433</a></td> </tr><tr> <td>[79]</td> <td class="space">DOI: 10.1016/j.automatica.2004.05.010 &middot; <a href="/1067.93031" class="nowrap">Zbl 1067.93031</a>&nbsp;&middot; <a href="https://doi.org/10.1016/j.automatica.2004.05.010" class="nowrap">doi:10.1016/j.automatica.2004.05.010</a></td> </tr><tr> <td>[80]</td> <td class="space">DOI: 10.1109/TAC.2005.854613 &middot; <a href="/1365.93561" class="nowrap">Zbl 1365.93561</a>&nbsp;&middot; <a href="https://doi.org/10.1109/TAC.2005.854613" class="nowrap">doi:10.1109/TAC.2005.854613</a></td> </tr><tr> <td>[81]</td> <td class="space">Xu, J-X and Yan, R. 2007. On Wavelet Learning Control for Affine Nonlinear Systems. Proceedings of American Control Conference. 2007. pp.1287&ndash;1292. New York</td> </tr><tr> <td>[82]</td> <td class="space">Xu J-X, IEEE Transactions on Neural Network 22 (2011)</td> </tr><tr> <td>[83]</td> <td class="space">DOI: 10.1109/9.793729 &middot; <a href="/0956.93027" class="nowrap">Zbl 0956.93027</a>&nbsp;&middot; <a href="https://doi.org/10.1109/9.793729" class="nowrap">doi:10.1109/9.793729</a></td> </tr><tr> <td>[84]</td> <td class="space">DOI: 10.1109/TSM.2002.807740&nbsp;&middot; <a href="https://doi.org/10.1109/TSM.2002.807740" class="nowrap">doi:10.1109/TSM.2002.807740</a></td> </tr><tr> <td>[85]</td> <td class="space">DOI: 10.1109/TAC.2010.2069372 &middot; <a href="/1368.93634" class="nowrap">Zbl 1368.93634</a>&nbsp;&middot; <a href="https://doi.org/10.1109/TAC.2010.2069372" class="nowrap">doi:10.1109/TAC.2010.2069372</a></td> </tr></table> <div class="reference_disclaimer"> 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. In some cases that data have been complemented/enhanced by data from zbMATH&nbsp;Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching. </div> </div></article> </div></div> </div> </div> <div class="clearfix"></div> </div> </div> <div id="foot"><div class="copyright"> &copy; 2025 <a target="fiz" href="https://www.fiz-karlsruhe.de/en">FIZ Karlsruhe GmbH</a> <a href="/privacy-policy/">Privacy Policy</a> <a href="/legal-notices/">Legal Notices</a> <a href="/terms-conditions/">Terms &amp; Conditions</a> <div class="info"> <ul class="nav"> <li class="mastodon"> <a href="https://mathstodon.xyz/@zbMATH" target="_blank" class="no-new-tab-icon"> <img src="/static/mastodon.png" title="zbMATH at Mathstodon (opens in new tab)" alt="Mastodon logo"> </a> </li> </ul> </div> </div> <div class="clearfix" style="height: 0px;"></div> </div> </div> <script src="https://static.zbmath.org/contrib/jquery/1.9.1/jquery.min.js"></script> <script src="https://static.zbmath.org/contrib/jquery-caret/1.5.2/jquery.caret.min.js"></script> <script src="/static/js/jquery-ui-1.10.1.custom.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap/v3.3.7zb1/js/bootstrap.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.js"></script> <script src="https://static.zbmath.org/contrib/retina/unknown/retina.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/js/bootstrap-select.min.js"></script> <script> var SCRIPT_ROOT = ""; </script> <script src="/static/scripts.js?v=20240926"> </script> <script src="https://static.zbmath.org/contrib/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ "HTML-CSS": { preferredFont: "TeX", availableFonts: [ "STIX", "TeX" ], linebreaks: { automatic: true }, EqnChunk: (MathJax.Hub.Browser.isMobile ? 10 : 50) }, tex2jax: { processEscapes: true, ignoreClass: "tex2jax_ignore|dno" }, TeX: { Macros: { Aut: "\\operatorname{Aut}", Hom: "\\operatorname{Hom}" }, noUndefined: { attributes: { mathcolor: "#039", //"red", mathbackground: "white", //"#FFEEEE", mathsize: "90%" } } }, messageStyle: "none" }); </script> <script type="text/javascript"> $(document).ready(function() { $("#MathInput").stop(true, true).keyup(function() { $.ajax({ url: "/mwsq/", type: "POST", data: { query : $("#MathInput").val() }, dataType: "text" }) .done(function(xml) { $("#MathPreview").html(xml); $(window).resize(); }); }); var press = jQuery.Event("keyup"); press.ctrlKey = false; press.which = 40; $("#MathInput").trigger(press); }); </script> <div id="new_tab_icon" style="display: none">&nbsp;<span class="glyphicon glyphicon-new-window" aria-hidden="true"></span><span class="sr-only">(opens in new tab)</span></div> </body> </html>

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