{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,20]],"date-time":"2026-01-20T10:23:02Z","timestamp":1768904582622,"version":"3.49.0"},"reference-count":43,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2019,1,10]],"date-time":"2019-01-10T00:00:00Z","timestamp":1547078400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>In this paper, a robust guaranteed-cost preview repetitive controller is proposed for a class of polytopic uncertain discrete-time systems. In order to improve the tracking performance, a repetitive controller, combined with preview compensator, is inserted in the forward channel. By using the L-order forward difference operator, an augmented dynamic system is constructed. Then, the guaranteed-cost preview repetitive control problem is transformed into a guaranteed-cost control problem for the augmented dynamic system. For a given performance index, the sufficient condition of asymptotic stability for the closed-loop system is derived by using a parameter-dependent Lyapunov function method and linear matrix inequality (LMI) techniques. Incorporating the controller obtained into the original system, the guaranteed-cost preview repetitive controller is derived. A numerical example is also included, to show the effectiveness of the proposed method.<\/jats:p>","DOI":"10.3390\/a12010020","type":"journal-article","created":{"date-parts":[[2019,1,11]],"date-time":"2019-01-11T04:10:16Z","timestamp":1547179816000},"page":"20","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["Robust Guaranteed-Cost Preview Repetitive Control for Polytopic Uncertain Discrete-Time Systems"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7072-4798","authenticated-orcid":false,"given":"Yong-Hong","family":"Lan","sequence":"first","affiliation":[{"name":"School of Information Engineering, Xiangtan University, Xiangtan 411105, China"}]},{"given":"Jun-Jun","family":"Xia","sequence":"additional","affiliation":[{"name":"School of Information Engineering, Xiangtan University, Xiangtan 411105, China"}]},{"given":"Yue-Xiang","family":"Shi","sequence":"additional","affiliation":[{"name":"School of Information Engineering, Xiangtan University, Xiangtan 411105, China"},{"name":"Led Lighting Research And Technology Center of Guizhou, Tongren 554300, China."}]}],"member":"1968","published-online":{"date-parts":[[2019,1,10]]},"reference":[{"key":"ref_1","first-page":"667","article-title":"Design of an optimal controller for a discrete-time system subject to previewable demand","volume":"23","author":"Katayama","year":"1985","journal-title":"Int. J. Control"},{"key":"ref_2","unstructured":"Tsuchiya, T., Tadashi, E., and Liao, T.b.F.C. (1994). Digital Preview and Predictive Control, Beijing Science and Technology Press."},{"key":"ref_3","first-page":"329","article-title":"Unified approach to optimal preview servo systems and optimal preview for compensated systems","volume":"10","author":"Liao","year":"1998","journal-title":"Chin. J. Autom."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"14188","DOI":"10.1016\/j.ifacol.2017.08.2086","article-title":"Flight test results of disturbance attenuation using preview feedforward compensation","volume":"50","author":"Hamada","year":"2017","journal-title":"IFAC-PapersOnLine"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/j.isatra.2018.01.005","article-title":"Robust preview control for a class of uncertain discrete-time systems with time-varying delay","volume":"73","author":"Li","year":"2018","journal-title":"ISA Trans."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/j.ast.2018.07.039","article-title":"Automatic carrier landing control for unmanned aerial vehicles based on preview control and particle filtering","volume":"81","author":"Zhen","year":"2018","journal-title":"Aerosp. Sci. Technol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1601","DOI":"10.1049\/iet-cta.2017.1280","article-title":"Reduced-order simultaneous state and fault estimator based fault tolerant preview control for discrete-time linear time-invariant systems","volume":"12","author":"Han","year":"2018","journal-title":"IET Control Theory Appl."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/j.conengprac.2013.12.007","article-title":"Optimal LQ feedforward tracking with preview: Practical design for rigid body motion control","volume":"26","author":"Matthew","year":"2014","journal-title":"Control Eng. Pract."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"176","DOI":"10.3182\/20140824-6-ZA-1003.01682","article-title":"The information structure of feedforward\/preview control using forecast data","volume":"47","author":"Robert","year":"2014","journal-title":"IFAC Proc."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1179","DOI":"10.1109\/TMECH.2015.2496343","article-title":"Constrained optimal preview control of dual-stage actuators","volume":"21","author":"Salton","year":"2016","journal-title":"IEEE\/ASME Trans. Mech."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"5115","DOI":"10.1016\/j.ifacol.2017.08.779","article-title":"Optimal feedforward preview control by fir filters","volume":"50","author":"Strohm","year":"2017","journal-title":"IFAC-PapersOnLine"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Jadidi, M.G., and Hashemi, E. (2016, January 12\u201315). Optimal preview control of the nao biped robot using a ukf-based state observer. Proceedings of the 2016 IEEE International Conference on Advanced Intelligent Mechatronics, Banff, AB, Canada.","DOI":"10.1109\/AIM.2016.7576742"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1002\/oca.2106","article-title":"Optimal preview control: A review","volume":"36","author":"Birla","year":"2015","journal-title":"Optim. Control Appl. Meth."},{"key":"ref_14","unstructured":"Takaba, K. (1998, January 23\u201325). Robust preview tracking control for polytopic uncertain systems. Proceedings of the 37th IEEE Conference on Decision and Control, Tampa, FL, USA."},{"key":"ref_15","unstructured":"Liao, F., Wan, J.L., and Yang, G.H. (2001, January 25\u201327). LMI-based reliable robust preview tracking control against actuator faults. Proceedings of the American Control Conference, Arlington, VA, USA."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"9932","DOI":"10.1016\/j.apm.2016.06.046","article-title":"Adaptive preview control for piecewise discrete-time systems using multiple models","volume":"40","author":"Wang","year":"2016","journal-title":"Appl. Math. Model."},{"key":"ref_17","first-page":"172","article-title":"Research development in preview control theory and applications","volume":"42","author":"Zhen","year":"2016","journal-title":"Acta Autom. Sin."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1049\/iet-cta.2016.0361","article-title":"Parameter-dependent preview control with robust tracking performance","volume":"11","author":"Li","year":"2017","journal-title":"IET Control Theory Appl."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Liao, F., and Li, L. (2017). Robust preview control for uncertain discrete-time systems based on LMI. Optim. Control Appl. Method.","DOI":"10.1002\/oca.2308"},{"key":"ref_20","unstructured":"Inoue, T., Nakano, M., and Iwai, S. (1981, January 24\u201328). High accuracy control of a proton synchrotron magnet power supply. Proceedings of the 8th Internat Fedaration on Automatic Control, Kyoto, Japan."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1016\/j.neucom.2018.01.064","article-title":"Observer-based H\u221e fuzzy control for modified repetitive control systems","volume":"286","author":"Wang","year":"2018","journal-title":"Neurocomputing"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1458","DOI":"10.1016\/S1474-6670(17)57872-6","article-title":"Discrete-time repetitive control of LTI systems sampled at a periodic rate","volume":"29","author":"Hanson","year":"1996","journal-title":"IFAC Proc."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"She, J.H., Pan, Y., and Nakano, M. (2000, January 7\u20139). Repetitive control system with variable structure controller. Proceedings of the 6th International Workshop on Variable Structure Systems, Gold Coast, Australia.","DOI":"10.1142\/9789812792082_0025"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"610","DOI":"10.1109\/TIE.2005.844227","article-title":"Variable-structure repetitive control: a discrete-time strategy","volume":"52","author":"Sun","year":"2005","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"308","DOI":"10.9746\/sicetr1965.33.308","article-title":"Discrete repetitive control via positive real compensation","volume":"33","author":"Fan","year":"2009","journal-title":"Trans. Soc. Instrum. Control Eng."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1007\/s11633-012-0629-1","article-title":"Design of discrete-time repetitive control system based on two-dimensionalmodel","volume":"9","author":"Yuan","year":"2012","journal-title":"Int. J. Autom. Comput."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1007\/s11633-013-0730-0","article-title":"Design of a design of a discrete-time output-feedback based repetitive-control system","volume":"10","author":"Zhou","year":"2013","journal-title":"Int. J. Autom. Comput."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"4236","DOI":"10.1007\/s11771-014-2420-7","article-title":"Design of observer-based discrete repetitive-control system based on 2D model","volume":"21","author":"Wang","year":"2014","journal-title":"J. Cent. South Univ."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1099","DOI":"10.1109\/TSMCC.2007.905759","article-title":"Iterative learning control: Brief survey and categorization","volume":"37","author":"Ahn","year":"2007","journal-title":"IEEE Trans. Syst. Man Cybern. C Appl. Rev."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1016\/j.conengprac.2017.05.004","article-title":"Robust guaranteed cost ILC with dynamic feedforward and disturbance compensation for accurate PMSM position control","volume":"65","author":"Mandra","year":"2017","journal-title":"Control Eng. Pract."},{"key":"ref_31","first-page":"1","article-title":"Performance-enhanced robust iterative learning control with experimental application to pmsm position tracking","volume":"1","author":"Mandra","year":"2018","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1016\/S0377-0427(02)00751-3","article-title":"Guaranteed cost stabilization of neutral differential systems with parametric uncertainty","volume":"151","author":"Park","year":"2003","journal-title":"Int. J. Comput. Appl. Math."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1016\/S0377-0427(03)00433-3","article-title":"Optimal guaranteed cost control of uncertain discrete time-delay systems","volume":"157","author":"Shi","year":"2004","journal-title":"Int. J. Comput. Appl. Math."},{"key":"ref_34","unstructured":"Fu, C., He, Y., Wu, M., and Yuan, S. (2010, January 29\u201331). Guaranteed cost robust discrete repetitive control based on two-dimension model. Proceedings of the 29th Chinese Control Conference, Beijing, China."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1002\/asjc.296","article-title":"Design of nonfragile guaranteed-cost repetitive-control system based on two-dimensional model","volume":"14","author":"Lan","year":"2012","journal-title":"Asian J. Control"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1080\/00423119208969008","article-title":"Optimal linear preview control of active vehicle suspension","volume":"21","author":"Aleksander","year":"1992","journal-title":"Veh. Syst. Dyn."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1463","DOI":"10.1016\/j.engstruct.2004.05.010","article-title":"Optimal preview active control of structures during earthquakes","volume":"26","author":"Marzbanrad","year":"2004","journal-title":"Eng. Struct."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1115\/1.3153060","article-title":"Analysis and synthesis of discrete-time repetitive controllers","volume":"111","author":"Tomizuka","year":"1989","journal-title":"Trans. ASME J. Dyn. Syst. Meas. Control"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Boyd, S., Ghaoui, L., and Feron, E. (1994). Linear Matrix Inequalities in System and Control Theory, SIAM Studies in Applied Mathematics.","DOI":"10.1137\/1.9781611970777"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"545","DOI":"10.1049\/iet-cta.2015.0750","article-title":"Robust output feedback controller design of discrete-time Takagi-Sugeno fuzzy systems: A nonmonotonic Lyapunov approach","volume":"10","author":"Nasiri","year":"2016","journal-title":"IET Control Theory Appl."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/j.fss.2014.10.023","article-title":"Robust static output feedback H\u221e control for uncertain fuzzy systems","volume":"273","author":"Chang","year":"2015","journal-title":"Fuzzy Sets Syst."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1016\/j.asoc.2015.12.023","article-title":"Adaptive PSO for optimal LQR tracking control of 2 DoF laboratory helicopter","volume":"41","author":"Kumar","year":"2016","journal-title":"Appl. Soft Comput."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"438","DOI":"10.1016\/j.epsr.2017.08.004","article-title":"GA-based robust LQR controller for interleaved boost DC-DC converter improving fuel cell voltage regulation","volume":"152","author":"Habib","year":"2017","journal-title":"Electr. Power Syst. Res."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/12\/1\/20\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:24:58Z","timestamp":1760185498000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/12\/1\/20"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1,10]]},"references-count":43,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2019,1]]}},"alternative-id":["a12010020"],"URL":"https:\/\/doi.org\/10.3390\/a12010020","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,1,10]]}}}