{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,4,19]],"date-time":"2024-04-19T16:09:41Z","timestamp":1713542981413},"reference-count":31,"publisher":"Walter de Gruyter GmbH","issue":"11","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,11,25]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Laser photocoagulation is a technique applied in the treatment of retinal disease, which is often done manually or using simple control schemes. We pursue an optimization-based approach, namely Model Predictive Control (MPC), to enforce bounds on the peak temperature and, thus, to ensure safety during the medical treatment procedure \u2013 despite the spot-dependent absorption of the tissue. The desired laser repetition rate of 1\u00a0kHz is renders the requirements on the computation time of the MPC feedback a major challenge. We present a tailored MPC scheme using parametric model reduction, an extended Kalman filter for the parameter and state estimation, and suitably tuned stage costs and verify its applicability both in simulation and experiments with porcine eyes. Moreover, we give some insight on the implementation specifically tailored for fast numerical computations.<\/jats:p>","DOI":"10.1515\/auto-2022-0030","type":"journal-article","created":{"date-parts":[[2022,11,15]],"date-time":"2022-11-15T12:37:37Z","timestamp":1668515857000},"page":"992-1002","source":"Crossref","is-referenced-by-count":2,"title":["Model predictive control for retinal laser treatment at 1 kHz"],"prefix":"10.1515","volume":"70","author":[{"given":"Manuel","family":"Schaller","sequence":"first","affiliation":[{"name":"Optimization-Based Control group , Institute of Mathematics, Technische Universit\u00e4t Ilmenau , Ilmenau , Germany"}]},{"given":"Viktoria","family":"Kleyman","sequence":"additional","affiliation":[{"name":"Institute of Automatic Control, Leibniz University Hannover , Hannover , Germany"}]},{"given":"Mario","family":"Mordm\u00fcller","sequence":"additional","affiliation":[{"name":"Institute of Biomedical Optics, University of L\u00fcbeck and Medical Laser Center L\u00fcbeck , L\u00fcbeck , Germany"}]},{"given":"Christian","family":"Schmidt","sequence":"additional","affiliation":[{"name":"Institute of Biomedical Optics, University of L\u00fcbeck and Medical Laser Center L\u00fcbeck , L\u00fcbeck , Germany"}]},{"given":"Mitsuru","family":"Wilson","sequence":"additional","affiliation":[{"name":"Optimization-Based Control group , Institute of Mathematics, Technische Universit\u00e4t Ilmenau , Ilmenau , Germany"}]},{"given":"Ralf","family":"Brinkmann","sequence":"additional","affiliation":[{"name":"Institute of Biomedical Optics, University of L\u00fcbeck and Medical Laser Center L\u00fcbeck , L\u00fcbeck , Germany"}]},{"given":"Matthias A.","family":"M\u00fcller","sequence":"additional","affiliation":[{"name":"Institute of Automatic Control, Leibniz University Hannover , Hannover , Germany"}]},{"given":"Karl","family":"Worthmann","sequence":"additional","affiliation":[{"name":"Optimization-Based Control group , Institute of Mathematics, Technische Universit\u00e4t Ilmenau , Ilmenau , Germany"}]}],"member":"374","published-online":{"date-parts":[[2022,11,16]]},"reference":[{"key":"2023033111302684602_j_auto-2022-0030_ref_001","doi-asserted-by":"crossref","unstructured":"G. Meyer-Schwickerath, \u201cLichtkoagulation,\u201d Albrecht von Graefes Archiv f\u00fcr Ophthalmologie, vol. 156, no. 1, pp. 2\u201334, 1954.","DOI":"10.1007\/BF00703328"},{"key":"2023033111302684602_j_auto-2022-0030_ref_002","doi-asserted-by":"crossref","unstructured":"Early Treatment Diabetic Retinopathy Study Research Group and others, \u201cEarly photocoagulation for diabetic retinopathy: ETDRS report number 9,\u201d Ophthalmology, vol.\u00a098, no.\u00a05, pp.\u00a0766\u2013785, 1991.","DOI":"10.1016\/S0161-6420(13)38011-7"},{"key":"2023033111302684602_j_auto-2022-0030_ref_003","doi-asserted-by":"crossref","unstructured":"Early Treatment Diabetic Retinopathy Study Research Group and others, \u201cPhotocoagulation for diabetic macular edema,\u201d Arch. Ophthalmol., vol.\u00a0103, pp.\u00a01796\u20131806, 1985.","DOI":"10.1001\/archopht.1985.01050120030015"},{"key":"2023033111302684602_j_auto-2022-0030_ref_004","doi-asserted-by":"crossref","unstructured":"J. K Luttrull and G. Dorin, \u201cSubthreshold diode micropulse laser photocoagulation (sdm) as invisible retinal phototherapy for diabetic macular edema: a review,\u201d Curr. Diabetes Rev., vol.\u00a08, no.\u00a04, pp.\u00a0274\u2013284, 2012. https:\/\/doi.org\/10.2174\/157339912800840523.","DOI":"10.2174\/157339912800840523"},{"key":"2023033111302684602_j_auto-2022-0030_ref_005","doi-asserted-by":"crossref","unstructured":"D. Lavinsky, C. Sramek, J. Wang, et al.., \u201cSubvisible retinal laser therapy: titration algorithm and tissue response,\u201d Retina, vol.\u00a034, no.\u00a01, pp.\u00a087\u201397, 2014. https:\/\/doi.org\/10.1097\/iae.0b013e3182993edc.","DOI":"10.1097\/IAE.0b013e3182993edc"},{"key":"2023033111302684602_j_auto-2022-0030_ref_006","doi-asserted-by":"crossref","unstructured":"R. Brinkmann, S. Koinzer, K. Schlott, L. Ptaszynski, and M. Bever, \u201cReal-time temperature determination during retinal photocoagulation on patients,\u201d J. Biomed. Opt., vol.\u00a017, no.\u00a06, p.\u00a0061219, 2012. https:\/\/doi.org\/10.1117\/1.jbo.17.6.061219.","DOI":"10.1117\/1.JBO.17.6.061219"},{"key":"2023033111302684602_j_auto-2022-0030_ref_007","doi-asserted-by":"crossref","unstructured":"L. Gr\u00fcne and J. Pannek, Nonlinear Model Predictive Control: Theory and Algorithms, London, Springer Verlag, 2016.","DOI":"10.1007\/978-3-319-46024-6"},{"key":"2023033111302684602_j_auto-2022-0030_ref_008","unstructured":"J. B. Rawlings, D. Q. Mayne, and M. Diehl, Model Predictive Control: Theory, Computation, and Design, vol. 2, Madison, WI, Nob Hill Publishing, 2017."},{"key":"2023033111302684602_j_auto-2022-0030_ref_009","doi-asserted-by":"crossref","unstructured":"A. Baade, C. von der Burchard, M. Lawin, et al.., \u201cPower-controlled temperature guided retinal laser therapy,\u201d J. Biomed. Opt., vol.\u00a022, no.\u00a011, p.\u00a0118001, 2017. https:\/\/doi.org\/10.1117\/1.jbo.22.11.118001.","DOI":"10.1117\/1.JBO.22.11.118001"},{"key":"2023033111302684602_j_auto-2022-0030_ref_010","doi-asserted-by":"crossref","unstructured":"C. Herzog, O. Thomsen, B. Schmarbeck, M. Siebert, and R. Brinkmann, \u201cTemperature-controlled laser therapy of the retina via robust adaptive H\u221e${\\mathcal{H}}_{\\infty }$ -control,\u201d Automatisierungstechnik, vol.\u00a066, no.\u00a012, pp.\u00a01051\u20131063, 2018. https:\/\/doi.org\/10.1515\/auto-2018-0066.","DOI":"10.1515\/auto-2018-0066"},{"key":"2023033111302684602_j_auto-2022-0030_ref_011","doi-asserted-by":"crossref","unstructured":"M. Schaller, M. Wilson, V. Kleyman, et al.., \u201cParameter estimation and model reduction for model predictive control in retinal laser treatment,\u201d Control Eng. Pract., vol.\u00a0128, p.\u00a0105320, 2022. https:\/\/doi.org\/10.1016\/j.conengprac.2022.105320.","DOI":"10.1016\/j.conengprac.2022.105320"},{"key":"2023033111302684602_j_auto-2022-0030_ref_012","doi-asserted-by":"crossref","unstructured":"V. Kleyman, H. Gernandt, K. Worthmann, H. S. Abbas, R. Brinkmann, and M. A. M\u00fcller, \u201cModeling and parameter identification for real-time temperature controlled retinal laser therapies,\u201d Automatisierungstechnik, vol. 68, pp. 953\u2013966, 2020. https:\/\/doi.org\/10.1515\/auto-2020-0074.","DOI":"10.1515\/auto-2020-0074"},{"key":"2023033111302684602_j_auto-2022-0030_ref_013","doi-asserted-by":"crossref","unstructured":"V. Kleyman, M. Schaller, M. Wilson, et al.., \u201cState and parameter estimation for model-based retinal laser treatment,\u201d IFAC-PapersOnLine, vol.\u00a054, no.\u00a06, pp.\u00a0244\u2013250, 2021. https:\/\/doi.org\/10.1016\/j.ifacol.2021.08.552.","DOI":"10.1016\/j.ifacol.2021.08.552"},{"key":"2023033111302684602_j_auto-2022-0030_ref_014","doi-asserted-by":"crossref","unstructured":"M. Mordm\u00fcller, V. Kleyman, M. Schaller, et al.., \u201cTowards temperature controlled retinal laser treament with a single 10 kHz laser,\u201d Adv. Opt. Technol., vol. 10, no. 6, pp. 423\u2013431, 2021.","DOI":"10.1515\/aot-2021-0041"},{"key":"2023033111302684602_j_auto-2022-0030_ref_015","doi-asserted-by":"crossref","unstructured":"S. Chaturantabut and D. C. Sorensen, \u201cNonlinear model reduction via discrete empirical interpolation,\u201d SIAM J. Sci. Comput., vol.\u00a032, no.\u00a05, pp.\u00a02737\u20132764, 2010. https:\/\/doi.org\/10.1137\/090766498.","DOI":"10.1137\/090766498"},{"key":"2023033111302684602_j_auto-2022-0030_ref_016","doi-asserted-by":"crossref","unstructured":"P. Benner, S. Gugercin, and K. Willcox, \u201cA survey of projection-based model reduction methods for parametric dynamical systems,\u201d SIAM Rev., vol.\u00a057, no.\u00a04, pp.\u00a0483\u2013531, 2015. https:\/\/doi.org\/10.1137\/130932715.","DOI":"10.1137\/130932715"},{"key":"2023033111302684602_j_auto-2022-0030_ref_017","doi-asserted-by":"crossref","unstructured":"C. K. Chui and G. Chen, Kalman Filtering, Berlin, Springer International Publishing, 2017.","DOI":"10.1007\/978-3-319-47612-4"},{"key":"2023033111302684602_j_auto-2022-0030_ref_018","doi-asserted-by":"crossref","unstructured":"B. Stellato, G. Banjac, P. Goulart, A. Bemporad, and S. Boyd, \u201cOSQP: an operator splitting solver for quadratic programs,\u201d Math. Program. Comput., vol.\u00a012, no.\u00a04, pp.\u00a0637\u2013672, 2020. https:\/\/doi.org\/10.1007\/s12532-020-00179-2.","DOI":"10.1007\/s12532-020-00179-2"},{"key":"2023033111302684602_j_auto-2022-0030_ref_019","unstructured":"V. Kleyman, M. Schaller, M. Mordm\u00fcller, et al.., \u201cState and parameter estimation for retinal laser treatment,\u201d 2022, Submitted, Preprint: arXiv:2203.12452."},{"key":"2023033111302684602_j_auto-2022-0030_ref_020","doi-asserted-by":"crossref","unstructured":"J. Lorenzetti, B. Landry, S. Singh, and M. Pavone, \u201cReduced order model predictive control for setpoint tracking,\u201d in 2019 18th European Control Conference (ECC), IEEE, 2019, pp.\u00a0299\u2013306.","DOI":"10.23919\/ECC.2019.8796005"},{"key":"2023033111302684602_j_auto-2022-0030_ref_021","doi-asserted-by":"crossref","unstructured":"M. Koegel and R. Findeisen, \u201cRobust output feedback model predictive control using reduced order models,\u201d IFAC-PapersOnLine, vol. 48\u20138, pp. 1008\u20131014, 2015. https:\/\/doi.org\/10.1016\/j.ifacol.2015.09.100.","DOI":"10.1016\/j.ifacol.2015.09.100"},{"key":"2023033111302684602_j_auto-2022-0030_ref_022","doi-asserted-by":"crossref","unstructured":"L. Gr\u00fcne, J. Pannek, M. Seehafer, and K. Worthmann, \u201cAnalysis of unconstrained nonlinear MPC schemes with time varying control horizon,\u201d SIAM J. Control Optim., vol.\u00a048, no.\u00a08, pp.\u00a04938\u20134962, 2010. https:\/\/doi.org\/10.1137\/090758696.","DOI":"10.1137\/090758696"},{"key":"2023033111302684602_j_auto-2022-0030_ref_023","doi-asserted-by":"crossref","unstructured":"L. Gr\u00fcne, J. Pannek, and K. Worthmann, \u201cA networked unconstrained nonlinear MPC scheme,\u201d in 2009 European Control Conference (ECC), IEEE, 2009, pp.\u00a0371\u2013376.","DOI":"10.23919\/ECC.2009.7074430"},{"key":"2023033111302684602_j_auto-2022-0030_ref_024","doi-asserted-by":"crossref","unstructured":"K. Worthmann, M. Reble, and F. Gr\u00fcne, \u201cLars an Allg\u00f6wer. The role of sampling for stability and performance in unconstrained nonlinear model predictive control,\u201d SIAM J. Control Optim., vol.\u00a052, no.\u00a01, pp.\u00a0581\u2013605, 2014. https:\/\/doi.org\/10.1137\/12086652x.","DOI":"10.1137\/12086652X"},{"key":"2023033111302684602_j_auto-2022-0030_ref_025","doi-asserted-by":"crossref","unstructured":"K. Worthmann, M. W. Mehrez, G. K. Mann, R. G. Gosine, and J. Pannek, \u201cInteraction of open and closed loop control in MPC,\u201d Automatica, vol.\u00a082, pp.\u00a0243\u2013250, 2017. https:\/\/doi.org\/10.1016\/j.automatica.2017.04.038.","DOI":"10.1016\/j.automatica.2017.04.038"},{"key":"2023033111302684602_j_auto-2022-0030_ref_026","doi-asserted-by":"crossref","unstructured":"L. Gr\u00fcne and V. G. Palma, \u201cRobustness of performance and stability for multistep and updated multistep MPC schemes,\u201d Discrete Contin. Dyn. Syst., vol.\u00a035, no.\u00a09, p.\u00a04385, 2015. https:\/\/doi.org\/10.3934\/dcds.2015.35.4385.","DOI":"10.3934\/dcds.2015.35.4385"},{"key":"2023033111302684602_j_auto-2022-0030_ref_027","doi-asserted-by":"crossref","unstructured":"V. G. Palma, A. Suardi, and E. C. Kerrigan, \u201cSensitivity-based multistep MPC for embedded systems,\u201d IFAC-PapersOnLine, vol.\u00a048, no.\u00a023, pp.\u00a0360\u2013365, 2015. https:\/\/doi.org\/10.1016\/j.ifacol.2015.11.306.","DOI":"10.1016\/j.ifacol.2015.11.306"},{"key":"2023033111302684602_j_auto-2022-0030_ref_028","doi-asserted-by":"crossref","unstructured":"M. Diehl, H. G. Bock, and J. P. Schl\u00f6der, \u201cA real-time iteration scheme for nonlinear optimization in optimal feedback control,\u201d SIAM J. Control Optim., vol.\u00a043, no.\u00a05, pp.\u00a01714\u20131736, 2005. https:\/\/doi.org\/10.1137\/s0363012902400713.","DOI":"10.1137\/S0363012902400713"},{"key":"2023033111302684602_j_auto-2022-0030_ref_029","doi-asserted-by":"crossref","unstructured":"A. Wynn, M. Vukov, and M. Diehl, \u201cConvergence guarantees for moving horizon estimation based on the real-time iteration scheme,\u201d IEEE Trans. Autom. Control, vol.\u00a059, no.\u00a08, pp.\u00a02215\u20132221, 2014. https:\/\/doi.org\/10.1109\/tac.2014.2298984.","DOI":"10.1109\/TAC.2014.2298984"},{"key":"2023033111302684602_j_auto-2022-0030_ref_030","doi-asserted-by":"crossref","unstructured":"A. Nurkanovi\u0107, A. Zanelli, S. Albrecht, and M. Diehl, \u201cThe advanced step real time iteration for NMPC,\u201d in 2019 IEEE 58th Conference on Decision and Control (CDC), IEEE, 2019, pp.\u00a05298\u20135305.","DOI":"10.1109\/CDC40024.2019.9029543"},{"key":"2023033111302684602_j_auto-2022-0030_ref_031","doi-asserted-by":"crossref","unstructured":"A. Nurkanovi\u0107, A. Zanelli, S. Albrecht, G. Frison, and M. Diehl, \u201cContraction properties of the advanced step real-time iteration for NMPC,\u201d IFAC-PapersOnLine, vol.\u00a053, no.\u00a02, pp.\u00a07041\u20137048, 2020. https:\/\/doi.org\/10.1016\/j.ifacol.2020.12.449.","DOI":"10.1016\/j.ifacol.2020.12.449"}],"container-title":["at - Automatisierungstechnik"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/auto-2022-0030\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/auto-2022-0030\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,31]],"date-time":"2023-03-31T15:02:37Z","timestamp":1680274957000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/auto-2022-0030\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11,1]]},"references-count":31,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2022,11,16]]},"published-print":{"date-parts":[[2022,11,25]]}},"alternative-id":["10.1515\/auto-2022-0030"],"URL":"https:\/\/doi.org\/10.1515\/auto-2022-0030","relation":{},"ISSN":["0178-2312","2196-677X"],"issn-type":[{"value":"0178-2312","type":"print"},{"value":"2196-677X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,11,1]]}}}