{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,28]],"date-time":"2025-03-28T11:29:03Z","timestamp":1743161343368,"version":"3.28.0"},"reference-count":34,"publisher":"Walter de Gruyter GmbH","issue":"8","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,8,28]]},"abstract":"<jats:title>Zusammenfassung<\/jats:title><jats:p>In vielen Anwendungen der Regelungstechnik werden Beobachter eingesetzt, um interne Zustandsgr\u00f6\u00dfen oder Parameter zu sch\u00e4tzen oder Fehler zu detektieren. Solche Beobachter lassen sich auch f\u00fcr nichtlineare Systeme systematisch auf Basis der Beobachter- oder der Beobachtbarkeitsnormalform entwerfen. Letztere existiert f\u00fcr eine gr\u00f6\u00dfere Systemklasse. Allerdings ist das Vektorfeld in der Beobachtbarkeitsnormalform nicht unbedingt an allen Punkten definiert oder Lipschitz-stetig, selbst wenn diese Eigenschaften auf die urspr\u00fcngliche Systemdarstellung zutreffen. Durch die Einbettung in h\u00f6herdimensionale R\u00e4ume ist es m\u00f6glich, die Normalform einerseits zu konstruieren und gegebenenfalls gewisse singul\u00e4re Punkte zu vermeiden. In diesem Beitrag wird gezeigt, wie dies systematisch f\u00fcr polynomiale Systeme mit mehreren Ein- oder Ausg\u00e4ngen bewerkstelligt werden kann.<\/jats:p>","DOI":"10.1515\/auto-2023-0065","type":"journal-article","created":{"date-parts":[[2023,8,8]],"date-time":"2023-08-08T15:44:47Z","timestamp":1691509487000},"page":"646-658","source":"Crossref","is-referenced-by-count":2,"title":["Einbettungsbeobachter f\u00fcr polynomiale Systeme"],"prefix":"10.1515","volume":"71","author":[{"given":"Daniel","family":"Gerbet","sequence":"first","affiliation":[{"name":"Institut f\u00fcr Regelungs- und Steuerungstheorie, Fakult\u00e4t Elektrotechnik und Informationstechnik , Technische Universit\u00e4t Dresden , 01062 Dresden , Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Klaus","family":"R\u00f6benack","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Regelungs- und Steuerungstheorie, Fakult\u00e4t Elektrotechnik und Informationstechnik , Technische Universit\u00e4t Dresden , 01062 Dresden , Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2023,8,8]]},"reference":[{"key":"2024011813340282201_j_auto-2023-0065_ref_001","doi-asserted-by":"crossref","unstructured":"R. E. Kalman and R. S. Bucy, \u201cNew results in linear filtering and prediction theory,\u201d Trans. ASME J. Basic Eng., vol.\u00a083D, no.\u00a01, pp.\u00a095\u2013108, 1961. https:\/\/doi.org\/10.1115\/1.3658902.","DOI":"10.1115\/1.3658902"},{"key":"2024011813340282201_j_auto-2023-0065_ref_002","doi-asserted-by":"crossref","unstructured":"D. G. Luenberger, \u201cObservers for multivariable systems,\u201d IEEE Trans. Automat. Control, vol.\u00a011, no.\u00a02, pp.\u00a0190\u2013197, 1966. https:\/\/doi.org\/10.1109\/tac.1966.1098323.","DOI":"10.1109\/TAC.1966.1098323"},{"key":"2024011813340282201_j_auto-2023-0065_ref_003","doi-asserted-by":"crossref","unstructured":"F. E. Thau, \u201cObserving the state of nonlinear dynamical systems,\u201d Int. J. Control, vol.\u00a017, no.\u00a03, pp.\u00a0471\u2013479, 1973. https:\/\/doi.org\/10.1080\/00207177308932395.","DOI":"10.1080\/00207177308932395"},{"key":"2024011813340282201_j_auto-2023-0065_ref_004","doi-asserted-by":"crossref","unstructured":"R. Rajamani, \u201cObservers for Lipschitz nonlinear systems,\u201d IEEE Trans. Automat. Control, vol.\u00a043, no.\u00a03, pp.\u00a0397\u2013401, 1998. https:\/\/doi.org\/10.1109\/9.661604.","DOI":"10.1109\/9.661604"},{"key":"2024011813340282201_j_auto-2023-0065_ref_005","doi-asserted-by":"crossref","unstructured":"K. R\u00f6benack, \u201cImproving high gain observer design for nonlinear systems using the structure of the linear part,\u201d in Systems, Automation & Control, N. Derbel, Ed., Berlin, Boston, De Gruyter Oldenbourg, 2016, pp.\u00a057\u201374.","DOI":"10.1515\/9783110448436-005"},{"key":"2024011813340282201_j_auto-2023-0065_ref_006","doi-asserted-by":"crossref","unstructured":"J. P. Gauthier, H. Hammouri, and S. Othman, \u201cA simple observer for nonlinear systems \u2013 application to bioreactors,\u201d IEEE Trans. Automat. Control, vol.\u00a037, no.\u00a06, pp.\u00a0875\u2013880, 1992. https:\/\/doi.org\/10.1109\/9.256352.","DOI":"10.1109\/9.256352"},{"key":"2024011813340282201_j_auto-2023-0065_ref_007","doi-asserted-by":"crossref","unstructured":"G. Ciccarella, M. D. Mora, and A. Germani, \u201cA Luenberger-like observer for nonlinear systems,\u201d Int. J. Control, vol.\u00a057, no.\u00a03, pp.\u00a0537\u2013556, 1993. https:\/\/doi.org\/10.1080\/00207179308934406.","DOI":"10.1080\/00207179308934406"},{"key":"2024011813340282201_j_auto-2023-0065_ref_008","doi-asserted-by":"crossref","unstructured":"D. Astolfi and L. Marconi, \u201cA high-gain nonlinear observer with limited gain power,\u201d IEEE Trans. Automat. Control, vol.\u00a060, no.\u00a011, pp.\u00a03059\u20133064, 2015. https:\/\/doi.org\/10.1109\/tac.2015.2408554.","DOI":"10.1109\/TAC.2015.2408554"},{"key":"2024011813340282201_j_auto-2023-0065_ref_009","doi-asserted-by":"crossref","unstructured":"M. Farza, A. Ragoubi, S. H. Sa\u00efd, and M M\u2019Saad, \u201cImproved high gain observer design for a class of disturbed nonlinear systems,\u201d Nonlinear Dynam., vol.\u00a0106, pp.\u00a0631\u2013655, 2021. https:\/\/doi.org\/10.1007\/s11071-021-06876-4.","DOI":"10.1007\/s11071-021-06876-4"},{"key":"2024011813340282201_j_auto-2023-0065_ref_010","doi-asserted-by":"crossref","unstructured":"A. Vargas, J. Moreno, and M. Zeitz, \u201cOrder extension of nonlinear systems for observer design under reduced observability properties,\u201d in 15th Triennial World Congress of the International Federation of Automatic Control Barcelona, 2002.","DOI":"10.3182\/20020721-6-ES-1901.00217"},{"key":"2024011813340282201_j_auto-2023-0065_ref_011","doi-asserted-by":"crossref","unstructured":"B. Tibken, \u201cObservability of nonlinear systems \u2013 an algebraic approach,\u201d in Proc. IEEE Conf. on Decision and Control (CDC), vol.\u00a05, Nassau, Bahamas, 2004, pp.\u00a04824\u20134825.","DOI":"10.1109\/CDC.2004.1429553"},{"key":"2024011813340282201_j_auto-2023-0065_ref_012","doi-asserted-by":"crossref","unstructured":"T. Paradowski, B. Tibken, and R. Swiatlak, \u201cAn approach to determine observability of nonlinear systems using interval analysis,\u201d in Proc. American Control Conference (ACC), Seattle, USA, 2017, pp.\u00a03932\u20133937.","DOI":"10.23919\/ACC.2017.7963557"},{"key":"2024011813340282201_j_auto-2023-0065_ref_013","doi-asserted-by":"crossref","unstructured":"K. R\u00f6benack and R. Vo\u00dfwinkel, \u201cFormal verification of local and global observability of polynomial systems using quantifier elimination,\u201d in International Conference on System Theory, Control and Computing (ICSTCC 2019), Sinaia, Romania, 2019, pp.\u00a0314\u2013319.","DOI":"10.1109\/ICSTCC.2019.8885899"},{"key":"2024011813340282201_j_auto-2023-0065_ref_014","doi-asserted-by":"crossref","unstructured":"J. Levine and R. Marino, \u201cNonlinear system immersion, observers and finite-dimensional filters,\u201d Syst. Control Lett., vol.\u00a07, pp.\u00a0133\u2013142, 1986. https:\/\/doi.org\/10.1016\/0167-6911(86)90019-8.","DOI":"10.1016\/0167-6911(86)90019-8"},{"key":"2024011813340282201_j_auto-2023-0065_ref_015","doi-asserted-by":"crossref","unstructured":"J. P. Gauthier, H. Hammouri, and I. Kupka, \u201cObservers for nonlinear systems,\u201d in Proc. IEEE Conf. on Decision and Control (CDC), England, Brighton, 1991, pp.\u00a01483\u20131489.","DOI":"10.1109\/CDC.1991.261648"},{"key":"2024011813340282201_j_auto-2023-0065_ref_016","doi-asserted-by":"crossref","unstructured":"A. Rapaport and A. Maloum, \u201cEmbedding for exponential observers of nonlinear systems,\u201d in Proc. of the 39th IEEE Conference on Decision and Control (CDC), vol.\u00a01, 2000, pp.\u00a0802\u2013803.","DOI":"10.1109\/CDC.2000.912867"},{"key":"2024011813340282201_j_auto-2023-0065_ref_017","unstructured":"J. M. Lee, Introduction to Smooth Manifolds, Volume 218 of Graduate Texts in Mathematics, New York, Springer, 2006."},{"key":"2024011813340282201_j_auto-2023-0065_ref_018","doi-asserted-by":"crossref","unstructured":"R. Hermann and A. J. Krener, \u201cNonlinear controllability and observability,\u201d IEEE Trans. Automat. Control, vol.\u00a022, no.\u00a05, pp.\u00a0728\u2013740, 1977. https:\/\/doi.org\/10.1109\/tac.1977.1101601.","DOI":"10.1109\/TAC.1977.1101601"},{"key":"2024011813340282201_j_auto-2023-0065_ref_019","doi-asserted-by":"crossref","unstructured":"E. D. Sontag, \u201cA concept of local observability,\u201d Syst. Control Lett., vol.\u00a05, pp.\u00a041\u201347, 1984. https:\/\/doi.org\/10.1016\/0167-6911(84)90007-0.","DOI":"10.1016\/0167-6911(84)90007-0"},{"key":"2024011813340282201_j_auto-2023-0065_ref_020","doi-asserted-by":"crossref","unstructured":"A. J. Krener and A. Isidori, \u201cLinearization by output injection and nonlinear observers,\u201d Syst. Control Lett., vol.\u00a03, pp.\u00a047\u201352, 1983. https:\/\/doi.org\/10.1016\/0167-6911(83)90037-3.","DOI":"10.1016\/0167-6911(83)90037-3"},{"key":"2024011813340282201_j_auto-2023-0065_ref_021","doi-asserted-by":"crossref","unstructured":"K. R\u00f6benack and A. F. Lynch, \u201cHigh-gain nonlinear observer design using the observer canonical form,\u201d IET Control Theory Appl., vol.\u00a01, no.\u00a06, pp.\u00a01574\u20131579, 2007. https:\/\/doi.org\/10.1049\/iet-cta:20060418.","DOI":"10.1049\/iet-cta:20060418"},{"key":"2024011813340282201_j_auto-2023-0065_ref_022","unstructured":"D. A. Cox, J. Little, and D. O\u2019Shea, Ideals, Varieties, and Algorithms, 4th ed., Switzerland, Springer International Publishing, 2015."},{"key":"2024011813340282201_j_auto-2023-0065_ref_023","unstructured":"T. Becker and V. Weispfenning, Gr\u00f6bner Bases, 2nd ed., New York, Springer-Verlag, 1998."},{"key":"2024011813340282201_j_auto-2023-0065_ref_024","doi-asserted-by":"crossref","unstructured":"J. Bochnak, M. Coste, and M. Roy, Real Algebraic Geometry, Berlin, Springer-Verlag, 1998.","DOI":"10.1007\/978-3-662-03718-8"},{"key":"2024011813340282201_j_auto-2023-0065_ref_025","doi-asserted-by":"crossref","unstructured":"D. Gerbet and K. R\u00f6benack, \u201cOn global and local observability of nonlinear polynomial systems: a decidable criterion,\u201d Automatisierungstechnik, vol.\u00a068, no.\u00a06, pp.\u00a0395\u2013409, 2020. https:\/\/doi.org\/10.1515\/auto-2020-0027.","DOI":"10.1515\/auto-2020-0027"},{"key":"2024011813340282201_j_auto-2023-0065_ref_026","doi-asserted-by":"crossref","unstructured":"M. Konz and J. Rudolph, \u201cBeispiele f\u00fcr einen direkten Zugang zu einer globalen, energiebasierten Modellbildung und Regelung von Starrk\u00f6rpersystemen,\u201d Automatisierungstechnik, vol.\u00a064, pp.\u00a096\u2013109, 2016. https:\/\/doi.org\/10.1515\/auto-2015-0095.","DOI":"10.1515\/auto-2015-0095"},{"key":"2024011813340282201_j_auto-2023-0065_ref_027","doi-asserted-by":"crossref","unstructured":"D. Gerbet and K. R\u00f6benack, \u201cA high-gain observer for embedded polynomial dynamical systems,\u201d Machines, vol.\u00a011, no.\u00a02, p.\u00a0190, 2023. https:\/\/doi.org\/10.3390\/machines11020190.","DOI":"10.3390\/machines11020190"},{"key":"2024011813340282201_j_auto-2023-0065_ref_028","doi-asserted-by":"crossref","unstructured":"J.-J. E. Slotine, J. K. Hedrick, and E. A. Misawa, \u201cNonlinear state estimation using sliding observers,\u201d in Proc. 25nd IEEE Conf. on Decision and Control (CDC), Athen, Griechenland, 1986, pp.\u00a0332\u2013339.","DOI":"10.1109\/CDC.1986.267257"},{"key":"2024011813340282201_j_auto-2023-0065_ref_029","doi-asserted-by":"crossref","unstructured":"J. K. H. J.-J. E. Slotine and E. A. Misawa, \u201cOn sliding observers for nonlinear systems,\u201d J. Dyn. Syst. Meas. Control, vol.\u00a0109, pp.\u00a0245\u2013252, 1987. https:\/\/doi.org\/10.1115\/1.3143852.","DOI":"10.1115\/1.3143852"},{"key":"2024011813340282201_j_auto-2023-0065_ref_030","doi-asserted-by":"crossref","unstructured":"S. K. Spurgeon, \u201cSliding mode obersers: a survey,\u201d Int. J. Syst. Sci., vol.\u00a039, no.\u00a08, pp.\u00a0751\u2013764, 2008. https:\/\/doi.org\/10.1080\/00207720701847638.","DOI":"10.1080\/00207720701847638"},{"key":"2024011813340282201_j_auto-2023-0065_ref_031","doi-asserted-by":"crossref","unstructured":"B. L. Walcott and S. H. Zak, \u201cObservation of dynamical systems in the presence of bounded nonlinearities\/uncertainties,\u201d in Proc. 25nd IEEE Conf. on Decision and Control (CDC), Athen, Griechenland, 1986, pp.\u00a0961\u2013966.","DOI":"10.1109\/CDC.1986.267514"},{"key":"2024011813340282201_j_auto-2023-0065_ref_032","doi-asserted-by":"crossref","unstructured":"L. E. Dickson, \u201cFiniteness of the odd perfect and primitive abundant numbers with n distinct prime factors,\u201d Am. J. Math., vol.\u00a035, pp.\u00a0413\u2013422, 1913. https:\/\/doi.org\/10.2307\/2370405.","DOI":"10.2307\/2370405"},{"key":"2024011813340282201_j_auto-2023-0065_ref_033","doi-asserted-by":"crossref","unstructured":"E. D. Sontag, Mathematical Control Theory, Volume 6 of Texts in Applied Mathematics, 2nd ed., New York, NY, Springer-Verlag, 1998.","DOI":"10.1007\/978-1-4612-0577-7"},{"key":"2024011813340282201_j_auto-2023-0065_ref_034","doi-asserted-by":"crossref","unstructured":"J.-P. Gauthier and I. Kupka, Deterministic Observation Theory and Applications, Cambridge, UK, Cambridge University Press, 2001.","DOI":"10.1017\/CBO9780511546648"}],"container-title":["at - Automatisierungstechnik"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/auto-2023-0065\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/auto-2023-0065\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,25]],"date-time":"2024-10-25T21:41:00Z","timestamp":1729892460000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/auto-2023-0065\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,8,1]]},"references-count":34,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2023,8,8]]},"published-print":{"date-parts":[[2023,8,28]]}},"alternative-id":["10.1515\/auto-2023-0065"],"URL":"https:\/\/doi.org\/10.1515\/auto-2023-0065","relation":{},"ISSN":["0178-2312","2196-677X"],"issn-type":[{"type":"print","value":"0178-2312"},{"type":"electronic","value":"2196-677X"}],"subject":[],"published":{"date-parts":[[2023,8,1]]}}}