{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,16]],"date-time":"2023-09-16T07:48:11Z","timestamp":1694850491721},"reference-count":39,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2019,4,29]],"date-time":"2019-04-29T00:00:00Z","timestamp":1556496000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,6,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This paper presents a method based on a continuity argument for analysing the delay robustness of nonlinear control systems with uncertainties. In particular, a delay-dependent stability condition is established in the form of a norm inequality for an adaptive control system with a time delay in the control input. The continuous dependence of the condition on the delay is derived via the uniform continuity in the delay of the fundamental solution of a general linear time-varying delay-differential equation. Since the stability condition holds when the delay is zero, the condition must be true for a certain non-zero positive delay due to continuity. Numerical simulations show the performance and robustness of the control system in the presence of an input delay. Remarkably, the results also illustrate a close agreement with the dependence on control parameters of the transient performance bounds predicted by the theoretical analysis in this paper.<\/jats:p>","DOI":"10.1093\/imamci\/dnz013","type":"journal-article","created":{"date-parts":[[2019,3,29]],"date-time":"2019-03-29T20:12:57Z","timestamp":1553890377000},"page":"559-588","source":"Crossref","is-referenced-by-count":1,"title":["Uniform continuity and delay robustness of an adaptive controller for Lagrangian systems"],"prefix":"10.1093","volume":"37","author":[{"given":"Kim-Doang","family":"Nguyen","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, South Dakota State University, USA"}]}],"member":"286","published-online":{"date-parts":[[2019,4,29]]},"reference":[{"key":"2020091709241846600_ref1","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-0653-8","volume-title":"Matrix Analysis","author":"Bhatia","year":"1997"},{"key":"2020091709241846600_ref2","first-page":"5397","article-title":"About robustness of internal model-based control for linear and nonlinear systems","volume-title":"57th IEEE Conference on Decision and Control","author":"Bin","year":"2018"},{"key":"2020091709241846600_ref3","doi-asserted-by":"crossref","first-page":"202","DOI":"10.1016\/j.automatica.2017.09.029","article-title":"On robustness analysis of linear vibrational control systems","volume":"87","author":"Cheng","year":"2018","journal-title":"Automatica J. IFAC"},{"key":"2020091709241846600_ref4","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1109\/LCSYS.2018.2867368","article-title":"Robustness analysis of a synthetic translational resource allocation controller","volume":"3","author":"Darlington","year":"2019","journal-title":"IEEE Control Syst. Lett."},{"key":"2020091709241846600_ref5","doi-asserted-by":"crossref","first-page":"1418","DOI":"10.2514\/1.56719","article-title":"Time-delay margin analysis for an adaptive controller","volume":"35","author":"Dorobantu","year":"2012","journal-title":"J. Guid. Control. Dynam."},{"key":"2020091709241846600_ref6","volume-title":"Modern Control Systems","author":"Dorf","year":"2011"},{"key":"2020091709241846600_ref39","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1109\/TAC.2008.916659","article-title":"Adaptive control and robustness in the gap metric","volume":"53","author":"French","year":"2008","journal-title":"IEEE Trans. Automat. Contr."},{"key":"2020091709241846600_ref7","first-page":"1045","article-title":"Projective lag synchronization of second-order chaotic systems via modified terminal sliding mode control","volume":"34","author":"Gao","year":"2017","journal-title":"IMA J. Math. Control Inform."},{"key":"2020091709241846600_ref8","doi-asserted-by":"crossref","first-page":"1200","DOI":"10.1109\/9.623082","article-title":"Robustness analysis of nonlinear feedback systems: an input-output approach","volume":"42","author":"Georgiou","year":"1997","journal-title":"IEEE Trans. Automat. Contr."},{"key":"2020091709241846600_ref9","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-4342-7","volume-title":"Introduction to Functional Differential Equations","author":"Hale","year":"1993"},{"key":"2020091709241846600_ref10","doi-asserted-by":"crossref","first-page":"334","DOI":"10.1109\/TSMC.2015.2429555","article-title":"Adaptive neural impedance control of a robotic manipulator with input saturation","volume":"46","author":"He","year":"2016","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."},{"key":"2020091709241846600_ref11","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898719376","volume-title":"Adaptive Control Theory: Guaranteed Robustness with Fast Adaptation","author":"Hovakimyan","year":"2010"},{"key":"2020091709241846600_ref12","doi-asserted-by":"crossref","first-page":"3169","DOI":"10.1137\/090758891","article-title":"Robustness of funnel control in the gap metric","volume":"48","author":"Ilchmann","year":"2010","journal-title":"SIAM J. Control Optim."},{"key":"2020091709241846600_ref13","volume-title":"Nonlinear Systems","author":"Khalil","year":"2002"},{"key":"2020091709241846600_ref14","article-title":"Projection operator in adaptive systems","author":"Lavretsky","year":"2011"},{"key":"2020091709241846600_ref15","doi-asserted-by":"crossref","DOI":"10.1201\/9780203026953","volume-title":"Robot Manipulator Control: Theory and Practice","author":"Lewis","year":"2003"},{"key":"2020091709241846600_ref16","doi-asserted-by":"crossref","first-page":"1625","DOI":"10.1137\/120903373","article-title":"Robust stability of input-output systems with initial conditions","volume":"53","author":"Liu","year":"2015","journal-title":"SIAM J. Control Optim."},{"key":"2020091709241846600_ref17","article-title":"Robust adaptive flight control systems in the presence of time delay","author":"Matsutani","year":"2013"},{"key":"2020091709241846600_ref18","doi-asserted-by":"crossref","DOI":"10.1201\/9781315136370","volume-title":"A Mathematical Introduction to Robotic Manipulation","author":"Murray","year":"2017"},{"key":"2020091709241846600_ref19","doi-asserted-by":"crossref","first-page":"997","DOI":"10.1093\/imamci\/dnv022","article-title":"On the robustness of linear and non-linear fractional-order systems with non-linear uncertain parameters","volume":"33","author":"N\u2019Doye","year":"2016","journal-title":"IMA J. Math. Control Inform."},{"key":"2020091709241846600_ref20","doi-asserted-by":"crossref","DOI":"10.2514\/6.2011-6438","article-title":"On time delay margin estimation for adaptive control and robust modification adaptive laws","volume-title":"AIAA Guidance, Navigation, and Control Conference, AIAA 2011\u20136438","author":"Nguyen","year":"2011"},{"key":"2020091709241846600_ref21","article-title":"Marginal stability in L1-adaptive control of manipulators","author":"Nguyen","year":"2013","journal-title":"ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference"},{"key":"2020091709241846600_ref22","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1109\/IROS.2014.6942549","article-title":"Synchronization and consensus of a robot network on an underactuated dynamic platform","volume-title":"IEEE\/RSJ International Conference on Intelligent Robots and Systems","author":"Nguyen","year":"2014"},{"key":"2020091709241846600_ref23","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1016\/j.robot.2014.10.009","article-title":"Adaptive control of underactuated robots with unmodeled dynamics","volume":"64","author":"Nguyen","year":"2015","journal-title":"Robotics Auton. Syst."},{"key":"2020091709241846600_ref24","first-page":"341","article-title":"A robust adaptive controller for a seed refilling system on a moving platform","volume":"49","author":"Nguyen","year":"2016","journal-title":"IFAC-PapersOnLine"},{"key":"2020091709241846600_ref25","doi-asserted-by":"crossref","first-page":"1433","DOI":"10.1002\/rnc.3624","article-title":"Cooperative control of networked robots on a dynamic platform in the presence of communication delays","volume":"27","author":"Nguyen","year":"2017","journal-title":"Int. J. Robust Nonlin. Control"},{"key":"2020091709241846600_ref26","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1016\/j.piutam.2017.08.003","article-title":"Delay robustness and compensation in L1 adaptive control","volume":"22","author":"Nguyen","year":"2017","journal-title":"Procedia IUTAM"},{"key":"2020091709241846600_ref27","doi-asserted-by":"crossref","first-page":"5485","DOI":"10.1109\/TAC.2017.2703913","article-title":"Delay robustness of an L1 adaptive controller for a class of systems with unknown matched nonlinearities","volume":"62","author":"Nguyen","year":"2017","journal-title":"IEEE Trans. Automat. Contr."},{"key":"2020091709241846600_ref28","doi-asserted-by":"crossref","first-page":"816","DOI":"10.1177\/0142331218771144","article-title":"On the adaptive control of spherical actuators","volume":"41","author":"Nguyen","year":"2019","journal-title":"Trans. Inst. Meas. Control"},{"key":"2020091709241846600_ref29","doi-asserted-by":"crossref","DOI":"10.1049\/iet-cta.2018.5953","article-title":"Input-delay compensation in a robust adaptive control framework","author":"Nguyen","year":"2019","journal-title":"IET Control Theory Appl."},{"key":"2020091709241846600_ref30","doi-asserted-by":"crossref","first-page":"126","DOI":"10.1115\/1.3139652","article-title":"Hybrid position\/force control of manipulators","volume":"103","author":"Raibert","year":"1981","journal-title":"J. Dyn. Syst. Meas. Control"},{"key":"2020091709241846600_ref31","doi-asserted-by":"crossref","first-page":"414","DOI":"10.1109\/TIE.2014.2327009","article-title":"Stability and robustness of disturbance-observer-based motion control systems","volume":"62","author":"Sariyildiz","year":"2015","journal-title":"IEEE Trans. Ind. Electron."},{"key":"2020091709241846600_ref32","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1177\/027836498700600303","article-title":"On the adaptive control of robot manipulators","volume":"6","author":"Slotine","year":"1987","journal-title":"Int. J. Rob. Res."},{"key":"2020091709241846600_ref33","volume-title":"Robot Modeling and Control","author":"Spong","year":"2006"},{"key":"2020091709241846600_ref34","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1093\/imamci\/dnu047","article-title":"Robust stochastic stabilization and ${\\mathscr{H}}_{\\infty } $ control of uncertain stochastic interval time-delay systems","volume":"33","author":"Wang","year":"2016","journal-title":"IMA J. Math. Control Inform."},{"key":"2020091709241846600_ref35","doi-asserted-by":"crossref","first-page":"948","DOI":"10.1109\/TAC.2016.2575827","article-title":"Adaptive control of robot manipulators with uncertain kinematics and dynamics","volume":"62","author":"Wang","year":"2017","journal-title":"IEEE Trans. Automat. Contr."},{"key":"2020091709241846600_ref36","doi-asserted-by":"crossref","first-page":"575","DOI":"10.1137\/0305036","article-title":"On the controllability of delay-differential systems","volume":"5","author":"Weiss","year":"1967","journal-title":"SIAM J. Control"},{"key":"2020091709241846600_ref37","first-page":"661","article-title":"Pad\u00e9-like approximation and its application in domain of attraction estimation","volume":"35","author":"Yaghmaei","year":"2017","journal-title":"IMA J. Math. Control Inform."},{"key":"2020091709241846600_ref38","doi-asserted-by":"crossref","first-page":"773","DOI":"10.1093\/imamci\/dnw077","article-title":"On the exponential stability of nonlinear delay systems with impulses","volume":"35","author":"You","year":"2018","journal-title":"IMA J. Math. Control Inform."}],"container-title":["IMA Journal of Mathematical Control and Information"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/academic.oup.com\/imamci\/article-pdf\/37\/2\/559\/33762526\/dnz013.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/academic.oup.com\/imamci\/article-pdf\/37\/2\/559\/33762526\/dnz013.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,15]],"date-time":"2023-09-15T04:16:41Z","timestamp":1694751401000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/imamci\/article\/37\/2\/559\/5480174"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,4,29]]},"references-count":39,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2019,4,29]]},"published-print":{"date-parts":[[2020,6,6]]}},"URL":"https:\/\/doi.org\/10.1093\/imamci\/dnz013","relation":{},"ISSN":["0265-0754","1471-6887"],"issn-type":[{"value":"0265-0754","type":"print"},{"value":"1471-6887","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2020,6]]},"published":{"date-parts":[[2019,4,29]]}}}