Document Zbl 1416.93178

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Control Signals Syst.</a> <a href="/?q=in%3A429702" title="Articles in this Issue">31, No. 2, Paper No. 8, 42 p. (2019)</a>. </div> <div class="abstract">Summary: Adaptive control deals with systems that have unknown and/or time-varying parameters. Most techniques are proven for the case in which any time variation is slow, with results for systems with fast time variations limited to those for which the time variation is of a known form or for which the plant has stable zero dynamics. In this paper, a new adaptive controller design methodology is proposed in which the time variation can be rapid and the plant may have unstable zero dynamics. Under the structural assumptions that the plant is relative degree one and that the plant uncertainty is a single scalar variable, as well as some mild regularity assumptions, it is proven that the closed-loop system is exponentially stable under fast parameter variations with persistent jumps. The proposed controller is nonlinear and periodic, and in each period the parameter is estimated and an appropriate stabilizing control signal is applied.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7073096">Cited in <strong>2</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A93D21" title="MSC2020">93D21</a> </td> <td class="space"> Adaptive or robust stabilization </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93C40" title="MSC2020">93C40</a> </td> <td class="space"> Adaptive control/observation systems </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93C05" title="MSC2020">93C05</a> </td> <td class="space"> Linear systems in control theory </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aadaptive+control">adaptive control</a>; <a href="/?q=ut%3Again+scheduling+control">gain scheduling control</a>; <a href="/?q=ut%3Atime-varying+plant">time-varying plant</a>; <a href="/?q=ut%3Aperiodic+control">periodic control</a></div>  <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">×</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;">  </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">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1416.93178" data-ciurl="/ci/07073096" data-biburl="/bibtex/07073096.bib" data-amsurl="/amsrefs/07073096.bib" data-xmlurl="/xml/07073096.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07073096.pdf" title="Zbl 1416.93178 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/10.1007/s00498-019-0236-6" aria-label="DOI for “Periodic adaptive stabilization of rapidly time-varying linear systems”" title="10.1007/s00498-019-0236-6">DOI</a> <a class="btn btn-default btn-xs" type="button" href="http://hdl.handle.net/10012/17488" title="Full Text Link">Link</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Goodwin GC, Ramadge PJ, Caines PE (1980) Discrete-time multivariable adaptive control. IEEE Trans Autom Control 25(3):449-456 · <a href="/0429.93034" class="nowrap">Zbl 0429.93034</a> · <a href="https://doi.org/10.1109/TAC.1980.1102363" class="nowrap">doi:10.1109/TAC.1980.1102363</a></td> </tr><tr> <td>[2]</td> <td class="space">Morse AS (1980) Global stability of parameter-adaptive control systems. IEEE Trans Autom Control 25(3):433-439 · <a href="/0438.93042" class="nowrap">Zbl 0438.93042</a> · <a href="https://doi.org/10.1109/TAC.1980.1102364" class="nowrap">doi:10.1109/TAC.1980.1102364</a></td> </tr><tr> <td>[3]</td> <td class="space">Narendra KS, Lin YH, Valavani LS (1980) Stable adaptive controller design, part II: proof of stability. IEEE Trans Autom Control 25(3):440-448 · <a href="/0467.93049" class="nowrap">Zbl 0467.93049</a> · <a href="https://doi.org/10.1109/TAC.1980.1102362" class="nowrap">doi:10.1109/TAC.1980.1102362</a></td> </tr><tr> <td>[4]</td> <td class="space">Rohrs CE, Valavani L, Athans M, Stein G (1985) Robustness of adaptive control algorithms in the presence of unmodeled dynamics. IEEE Trans Autom Control 30(9):881-889 · <a href="/0571.93042" class="nowrap">Zbl 0571.93042</a> · <a href="https://doi.org/10.1109/TAC.1985.1104070" class="nowrap">doi:10.1109/TAC.1985.1104070</a></td> </tr><tr> <td>[5]</td> <td class="space">Ioannou PA, Sun J (1996) Robust adaptive control. Prentice-Hall, Englewood Cliffs · <a href="/0839.93002" class="nowrap">Zbl 0839.93002</a></td> </tr><tr> <td>[6]</td> <td class="space">Byrnes CI, Willems JC (1984) Adaptive stabilization of multivariable linear systems. In: The 23rd IEEE conference on decision and control vol 23, 1574-1577</td> </tr><tr> <td>[7]</td> <td class="space">Miller DE, Davison EJ (1991) An adaptive controller which provides arbitrarily good transient and steady-state response. IEEE Trans Autom Control 36(1):68-81 · <a href="/0725.93074" class="nowrap">Zbl 0725.93074</a> · <a href="https://doi.org/10.1109/9.62269" class="nowrap">doi:10.1109/9.62269</a></td> </tr><tr> <td>[8]</td> <td class="space">Morse AS (1996) Supervisory control of families of linear set-point controllers—part I: exact matching. IEEE Trans Autom Control 41(10):1413-1431 · <a href="/0872.93009" class="nowrap">Zbl 0872.93009</a> · <a href="https://doi.org/10.1109/9.539424" class="nowrap">doi:10.1109/9.539424</a></td> </tr><tr> <td>[9]</td> <td class="space">Morse AS (1997) Supervisory control of families of linear set-point controllers—part II: robustness. IEEE Trans Autom Control 42(11):1500-1515 · <a href="/0926.93010" class="nowrap">Zbl 0926.93010</a> · <a href="https://doi.org/10.1109/9.649687" class="nowrap">doi:10.1109/9.649687</a></td> </tr><tr> <td>[10]</td> <td class="space">Narendra KS, Balakrishnan J (1997) Adaptive control using multiple models. IEEE Trans Autom Control 42(2):171-187 · <a href="/0869.93025" class="nowrap">Zbl 0869.93025</a> · <a href="https://doi.org/10.1109/9.554398" class="nowrap">doi:10.1109/9.554398</a></td> </tr><tr> <td>[11]</td> <td class="space">Hocherman-Frommer J, Kulkarni SR, Ramadge PJ (1998) Controller switching based on output prediction errors. IEEE Trans Autom Control 43(5):596-607 · <a href="/0911.93037" class="nowrap">Zbl 0911.93037</a> · <a href="https://doi.org/10.1109/9.668827" class="nowrap">doi:10.1109/9.668827</a></td> </tr><tr> <td>[12]</td> <td class="space">Hespanha JP, Liberzon D, Morse AS (2003) Overcoming the limitations of adaptive control by means of logic based switching. Syst Control Lett 49(1):49-65 · <a href="/1157.93440" class="nowrap">Zbl 1157.93440</a> · <a href="https://doi.org/10.1016/S0167-6911(02)00342-0" class="nowrap">doi:10.1016/S0167-6911(02)00342-0</a></td> </tr><tr> <td>[13]</td> <td class="space">Kreisselmeir G (1986) Adaptive control of a class of slowly time-varying plants. Syst Control Lett 8(2):97-103 · <a href="/0615.93040" class="nowrap">Zbl 0615.93040</a> · <a href="https://doi.org/10.1016/0167-6911(86)90067-8" class="nowrap">doi:10.1016/0167-6911(86)90067-8</a></td> </tr><tr> <td>[14]</td> <td class="space">Middleton RH, Goodwin GC (1988) Adaptive control of time-varying linear systems. IEEE Trans Autom Control 33(2):150-155 · <a href="/0637.93041" class="nowrap">Zbl 0637.93041</a> · <a href="https://doi.org/10.1109/9.382" class="nowrap">doi:10.1109/9.382</a></td> </tr><tr> <td>[15]</td> <td class="space">Tsakalis KS, Ioannou PA (1989) Adaptive control of linear time-varying plants: a new model reference controller structure. IEEE Trans Autom Control 34(10):1038-1046 · <a href="/0695.93029" class="nowrap">Zbl 0695.93029</a> · <a href="https://doi.org/10.1109/9.35273" class="nowrap">doi:10.1109/9.35273</a></td> </tr><tr> <td>[16]</td> <td class="space">Voulgaris PG, Dahleh MA, Valavani LS (1994) Robust adaptive control: a slowly varying systems approach. Automatica 30(9):1455-1461 · <a href="/0925.93446" class="nowrap">Zbl 0925.93446</a> · <a href="https://doi.org/10.1016/0005-1098(94)90011-6" class="nowrap">doi:10.1016/0005-1098(94)90011-6</a></td> </tr><tr> <td>[17]</td> <td class="space">Dimogianopoulos D, Lozano R (2001) Adaptive control for linear slowly time-varying systems using direct least-squares estimation. Automatica 37(2):251-256 · <a href="/0976.93045" class="nowrap">Zbl 0976.93045</a> · <a href="https://doi.org/10.1016/S0005-1098(00)00159-X" class="nowrap">doi:10.1016/S0005-1098(00)00159-X</a></td> </tr><tr> <td>[18]</td> <td class="space">Fidan B, Zhang Y, Ioannou P (2005) Adaptive control of a class of slowly time-varying systems with modelling uncertainties. IEEE Trans Autom Control 50(6):915-920 · <a href="/1365.93234" class="nowrap">Zbl 1365.93234</a> · <a href="https://doi.org/10.1109/TAC.2005.849259" class="nowrap">doi:10.1109/TAC.2005.849259</a></td> </tr><tr> <td>[19]</td> <td class="space">Vu L, Liberzon D (2011) Supervisory control of uncertain linear time-varying systems. IEEE Trans Autom Control 56(1):27-42 · <a href="/1368.93632" class="nowrap">Zbl 1368.93632</a> · <a href="https://doi.org/10.1109/TAC.2010.2060244" class="nowrap">doi:10.1109/TAC.2010.2060244</a></td> </tr><tr> <td>[20]</td> <td class="space">Vale JR, Miller DE (2011) Step tracking in the presence of persistent plant changes. IEEE Trans Autom Control 56(1):43-58 · <a href="/1368.93572" class="nowrap">Zbl 1368.93572</a> · <a href="https://doi.org/10.1109/TAC.2010.2051065" class="nowrap">doi:10.1109/TAC.2010.2051065</a></td> </tr><tr> <td>[21]</td> <td class="space">Miller DE, Vale JR (2014) Pole placement adaptive control with persistent jumps in the plant parameters. Math Control Signals Syst 16:177-214 · <a href="/1290.93081" class="nowrap">Zbl 1290.93081</a> · <a href="https://doi.org/10.1007/s00498-013-0115-5" class="nowrap">doi:10.1007/s00498-013-0115-5</a></td> </tr><tr> <td>[22]</td> <td class="space">Tsakalis KS, Ioannou PA (1990) A new indirect adaptive control scheme for time-varying plants. IEEE Trans Autom Control 35(6):697-705 · <a href="/0800.93652" class="nowrap">Zbl 0800.93652</a> · <a href="https://doi.org/10.1109/9.53548" class="nowrap">doi:10.1109/9.53548</a></td> </tr><tr> <td>[23]</td> <td class="space">Tian Z, Narendra KS (2009) Adaptive control of linear periodic systems. 2009 American Control Conference, June 2009</td> </tr><tr> <td>[24]</td> <td class="space">Annaswamy AM, Narendra KS (1989) Adaptive control of a first order plant with a time-varying parameter. American Control Conference, pp 975-980</td> </tr><tr> <td>[25]</td> <td class="space">Miller DE (2003) A new approach to model reference adaptive control. IEEE Trans Autom Control 48(5):743-757 · <a href="/1364.93403" class="nowrap">Zbl 1364.93403</a> · <a href="https://doi.org/10.1109/TAC.2003.811251" class="nowrap">doi:10.1109/TAC.2003.811251</a></td> </tr><tr> <td>[26]</td> <td class="space">Ilchmann A, Ryan EP, Trenn S (2005) Tracking control: performance funnels and prescribed transient behaviour. Syst Control Lett 54(7):655-670 · <a href="/1129.93503" class="nowrap">Zbl 1129.93503</a> · <a href="https://doi.org/10.1016/j.sysconle.2004.11.005" class="nowrap">doi:10.1016/j.sysconle.2004.11.005</a></td> </tr><tr> <td>[27]</td> <td class="space">Hackl CM, Hopfe N, Ilchmann A, Mueller M, Trenn S (2013) Funnel control for systems with relative degree two. SIAM J Control Optim 51(2):965-995 · <a href="/1267.93074" class="nowrap">Zbl 1267.93074</a> · <a href="https://doi.org/10.1137/100799903" class="nowrap">doi:10.1137/100799903</a></td> </tr><tr> <td>[28]</td> <td class="space">Marino R, Tomei P (2003) Adaptive control of linear time-varying systems. Automatica 39(4):651-659 · <a href="/1016.93035" class="nowrap">Zbl 1016.93035</a> · <a href="https://doi.org/10.1016/S0005-1098(02)00287-X" class="nowrap">doi:10.1016/S0005-1098(02)00287-X</a></td> </tr><tr> <td>[29]</td> <td class="space">Miller DE, Mansouri N (2010) Model reference adaptive control using simultaneous probing, estimation, and control. IEEE Trans Autom Control 55(9):2014-2029 · <a href="/1368.93307" class="nowrap">Zbl 1368.93307</a> · <a href="https://doi.org/10.1109/TAC.2010.2042983" class="nowrap">doi:10.1109/TAC.2010.2042983</a></td> </tr><tr> <td>[30]</td> <td class="space">Rudko V, Miller D (2016) Nonlinear periodic adaptive control for linear time-varying plants. American Control Conference</td> </tr><tr> <td>[31]</td> <td class="space">Rugh WJ (1991) Analytical framework for gain scheduling. IEEE Control Syst 11(1):79-84 · <a href="https://doi.org/10.1109/37.103361" class="nowrap">doi:10.1109/37.103361</a></td> </tr><tr> <td>[32]</td> <td class="space">Shamma JS, Athans M (1990) Analysis of gain scheduled control for nonlinear plants. IEEE Trans Autom Control 35(8):898-907 · <a href="/0723.93022" class="nowrap">Zbl 0723.93022</a> · <a href="https://doi.org/10.1109/9.58498" class="nowrap">doi:10.1109/9.58498</a></td> </tr><tr> <td>[33]</td> <td class="space">Rugh WJ, Shamma JS (2000) Research on gain scheduling. Automatica 36:1401-1425 · <a href="/0976.93002" class="nowrap">Zbl 0976.93002</a> · <a href="https://doi.org/10.1016/S0005-1098(00)00058-3" class="nowrap">doi:10.1016/S0005-1098(00)00058-3</a></td> </tr><tr> <td>[34]</td> <td class="space">Blanchini F (1991) Ultimate boundedness control for uncertain discrete-time systems via set-induced lyapunov functions. In: Proceeding of the 30th IEEE conference on decision and control, vol 2, 1755-1760</td> </tr><tr> <td>[35]</td> <td class="space">Blanchini F (1995) Nonquadratic lyapunov functions for robust control. Automatica 31(3):451-461 · <a href="/0825.93653" class="nowrap">Zbl 0825.93653</a> · <a href="https://doi.org/10.1016/0005-1098(94)00133-4" class="nowrap">doi:10.1016/0005-1098(94)00133-4</a></td> </tr><tr> <td>[36]</td> <td class="space">Blanchini F (2000) The gain scheduling and the robust state feedback stabilization problems. IEEE Trans Autom Control 45(11):2061-2070 · <a href="/0991.93102" class="nowrap">Zbl 0991.93102</a> · <a href="https://doi.org/10.1109/9.887627" class="nowrap">doi:10.1109/9.887627</a></td> </tr><tr> <td>[37]</td> <td class="space">Blanchini F, Miani S, Savorgnan C (2007) Stability results for linear parameter varying and switching systems. Automatica 43(10):1817-1823 · <a href="/1119.93062" class="nowrap">Zbl 1119.93062</a> · <a href="https://doi.org/10.1016/j.automatica.2007.03.002" class="nowrap">doi:10.1016/j.automatica.2007.03.002</a></td> </tr><tr> <td>[38]</td> <td class="space">Blanchini F, Casagrande D, Miani S, Viaro U (2010) Stable LPV realization of parametric transfer functions and its application to gain-scheduling control design. IEEE Trans Autom Control 55(10):2271-2281 · <a href="/1368.93528" class="nowrap">Zbl 1368.93528</a> · <a href="https://doi.org/10.1109/TAC.2010.2044259" class="nowrap">doi:10.1109/TAC.2010.2044259</a></td> </tr><tr> <td>[39]</td> <td class="space">Miller DE (2006) Near optimal LQR performance for a compact set of plants. IEEE Trans Autom Control 51(9):1423-1439 · <a href="/1366.93141" class="nowrap">Zbl 1366.93141</a> · <a href="https://doi.org/10.1109/TAC.2006.880961" class="nowrap">doi:10.1109/TAC.2006.880961</a></td> </tr><tr> <td>[40]</td> <td class="space">Rudko V (2013) Nonlinear period adaptive control for linear time-varying plants. Master’s thesis, University of Waterloo, Canada. Available: https://uwspace.uwaterloo.ca/handle/10012/7775</td> </tr><tr> <td>[41]</td> <td class="space">Vidyasagar M (1985) Control system synthesis: a factorization approach. The MIT Press, Cambridge · <a href="/0655.93001" class="nowrap">Zbl 0655.93001</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 Open. 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