{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,12]],"date-time":"2026-03-12T02:57:51Z","timestamp":1773284271465,"version":"3.50.1"},"reference-count":42,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2019,4,16]],"date-time":"2019-04-16T00:00:00Z","timestamp":1555372800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Robotica"],"published-print":{"date-parts":[[2020,1]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>The article proposes a nonlinear optimal control method for the model of the wheeled inverted pendulum (WIP). This is a difficult control and robotics problem due to the system\u2019s strong nonlinearities and due to its underactuation. First, the dynamic model of the WIP undergoes approximate linearization around a temporary operating point which is recomputed at each time step of the control method. The linearization procedure makes use of Taylor series expansion and of the computation of the associated Jacobian matrices. For the linearized model of the wheeled pendulum, an optimal (<jats:italic>H<\/jats:italic>-infinity) feedback controller is developed. The controller\u2019s gain is computed through the repetitive solution of an algebraic Riccati equation at each iteration of the control algorithm. The global asymptotic stability properties of the control method are proven through Lyapunov analysis. Finally, by using the <jats:italic>H<\/jats:italic>-infinity Kalman Filter as a robust state estimator, the implementation of a state estimation-based control scheme becomes also possible.<\/jats:p>","DOI":"10.1017\/s0263574719000456","type":"journal-article","created":{"date-parts":[[2019,4,16]],"date-time":"2019-04-16T04:46:21Z","timestamp":1555389981000},"page":"29-47","source":"Crossref","is-referenced-by-count":33,"title":["Nonlinear Optimal Control for the Wheeled Inverted Pendulum System"],"prefix":"10.1017","volume":"38","author":[{"given":"G.","family":"Rigatos","sequence":"first","affiliation":[]},{"given":"K.","family":"Busawon","sequence":"additional","affiliation":[]},{"given":"J.","family":"Pomares","sequence":"additional","affiliation":[]},{"given":"M.","family":"Abbaszadeh","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2019,4,16]]},"reference":[{"key":"S0263574719000456_ref24","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-16420-5"},{"key":"S0263574719000456_ref38","doi-asserted-by":"publisher","DOI":"10.23919\/ACC.2018.8431624"},{"key":"S0263574719000456_ref40","doi-asserted-by":"publisher","DOI":"10.1016\/j.promfg.2018.02.116"},{"key":"S0263574719000456_ref10","doi-asserted-by":"publisher","DOI":"10.1109\/TCST.2014.2300171"},{"key":"S0263574719000456_ref8","doi-asserted-by":"publisher","DOI":"10.1016\/j.robot.2015.02.012"},{"key":"S0263574719000456_ref39","doi-asserted-by":"publisher","DOI":"10.1109\/ACCESS.2018.2859840"},{"key":"S0263574719000456_ref42","doi-asserted-by":"publisher","DOI":"10.1016\/j.mechatronics.2015.06.011"},{"key":"S0263574719000456_ref41","doi-asserted-by":"publisher","DOI":"10.1109\/TIE.2014.2327562"},{"key":"S0263574719000456_ref37","doi-asserted-by":"publisher","DOI":"10.1109\/TSMC.2016.2621181"},{"key":"S0263574719000456_ref34","unstructured":"34. Z. J. Wang and F. C. Wang , \u201cThe Development and Control of a Two-Wheeled Inverted Pendulum,\u201d Proceedings of the IEEE SICE 2017 International Conference, Kanazawa, Japan (2017, September)."},{"key":"S0263574719000456_ref35","doi-asserted-by":"publisher","DOI":"10.1016\/j.ifacol.2018.06.042"},{"key":"S0263574719000456_ref36","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2017.2760283"},{"key":"S0263574719000456_ref31","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0027676"},{"key":"S0263574719000456_ref1","doi-asserted-by":"publisher","DOI":"10.1109\/TCST.2015.2404897"},{"key":"S0263574719000456_ref28","volume-title":"Detection of Abrupt Changes: Theory and Applications","author":"Basseville","year":"1993"},{"key":"S0263574719000456_ref26","doi-asserted-by":"publisher","DOI":"10.1080\/15325008.2015.1092056"},{"key":"S0263574719000456_ref25","volume-title":"Intelligent Renewable Energy systems: Modelling and Control","author":"Rigatos","year":"2017"},{"key":"S0263574719000456_ref21","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2016.01.008"},{"key":"S0263574719000456_ref33","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2005.861732"},{"key":"S0263574719000456_ref6","doi-asserted-by":"publisher","DOI":"10.1109\/TIE.2009.2027252"},{"key":"S0263574719000456_ref22","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2015.08.013"},{"key":"S0263574719000456_ref9","doi-asserted-by":"publisher","DOI":"10.1109\/TRO.2013.2239555"},{"key":"S0263574719000456_ref13","doi-asserted-by":"publisher","DOI":"10.1109\/TRO.2010.2053732"},{"key":"S0263574719000456_ref29","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2008.07.008"},{"key":"S0263574719000456_ref12","doi-asserted-by":"publisher","DOI":"10.1109\/TCST.2012.2214439"},{"key":"S0263574719000456_ref5","doi-asserted-by":"publisher","DOI":"10.1109\/TCST.2011.2168224"},{"key":"S0263574719000456_ref3","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-015-2376-7"},{"key":"S0263574719000456_ref14","doi-asserted-by":"publisher","DOI":"10.1016\/j.mechatronics.2015.06.011"},{"key":"S0263574719000456_ref11","doi-asserted-by":"publisher","DOI":"10.1109\/TIE.2013.2282594"},{"key":"S0263574719000456_ref16","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2014.2302475"},{"key":"S0263574719000456_ref15","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-015-0759-z"},{"key":"S0263574719000456_ref4","doi-asserted-by":"publisher","DOI":"10.1109\/TCST.2015.2417499"},{"key":"S0263574719000456_ref2","unstructured":"2. S. Ri , J. Huang , C. Tao , M. Ri , Y. Ri and D. Han , \u201cA High-Order Disturbance Observer Based Sliding Mode Velocity Control of Mobile Wheeled Inverted Pendulum Systems,\u201d IEEE 12th International World Congress on Intelligent Contorl and Automation, IEEE WCICA 2016, Guilin, China (2014, June)."},{"key":"S0263574719000456_ref7","doi-asserted-by":"publisher","DOI":"10.1109\/TRO.2004.840905"},{"key":"S0263574719000456_ref17","doi-asserted-by":"publisher","DOI":"10.1109\/TIE.2009.2039452"},{"key":"S0263574719000456_ref27","doi-asserted-by":"publisher","DOI":"10.1080\/01443610500212468"},{"key":"S0263574719000456_ref18","doi-asserted-by":"publisher","DOI":"10.1109\/TIE.2010.2102318"},{"key":"S0263574719000456_ref30","unstructured":"30. G. J. Toussaint , T. Basar and F. Bullo , \u201cH \u221e Optimal Tracking Control Techniques for Nonlinear Underactuated Systems,\u201d Proceedings of IEEE CDC 2000, 39th IEEE Conference on Decision and Control, Sydney, Australia (2000, December)."},{"key":"S0263574719000456_ref19","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1109\/TCST.2008.924579","article-title":"Adaptive robust dynamic balance and motion controls of mobile wheeled inverted pendulums","volume":"17","author":"Li","year":"2009","journal-title":"IEEE Trans. Control Syst. 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