{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T13:31:55Z","timestamp":1787232715607,"version":"build-2736575974"},"reference-count":32,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM Rev."],"published-print":{"date-parts":[[2007,1]]},"abstract":"<jats:p>We propose a novel approach for the parametrically robust design of dynamic systems. The approach can be applied to system models with parameters that are uncertain in the sense that values for these parameters are not known precisely, but only within certain bounds. The novel approach is guaranteed to find an optimal steady state that is stable for each parameter combination within these bounds. Our approach combines the use of a standard solver for constrained optimization problems with the rigorous solution of nonlinear systems. The constraints for the optimization problems are based on the concept of parameter space normal vectors that measure the distance of a tentative optimum to the nearest known critical point, i.e., a point where stability may be lost. Such normal vectors are derived using methods from nonlinear dynamics. After the optimization, the rigorous solver is used to provide a guarantee that no critical points exist in the vicinity of the optimum, or to detect such points. In the latter case, the optimization is resumed, taking the newly found critical points into account. This optimize\u2010and\u2010verify procedure is repeated until the rigorous nonlinear solver can guarantee that the vicinity of the optimum is free from critical points and therefore the optimum is parametrically robust. In contrast to existing design methodologies, our approach can be automated and does not rely on the experience of the designing engineer. A simple model of a fermenter is used to illustrate the concepts and the order of activities arising in a typical design process.<\/jats:p>","DOI":"10.1137\/s003614450444662x","type":"journal-article","created":{"date-parts":[[2007,4,30]],"date-time":"2007-04-30T18:00:35Z","timestamp":1177956035000},"page":"236-254","source":"Crossref","is-referenced-by-count":21,"title":["A Hybrid Approach for Efficient Robust Design of Dynamic Systems"],"prefix":"10.1137","volume":"49","author":[{"given":"Martin","family":"M\u00f6nnigmann","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wolfgang","family":"Marquardt","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Christian H.","family":"Bischof","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Thomas","family":"Beelitz","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bruno","family":"Lang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Paul","family":"Willems","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2007,5,1]]},"reference":[{"key":"R1","unstructured":"G. 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Kearfott,\n                      Rigorous Global Search: Continuous Problems\n                      , Kluwer Academic, Dordrecht, The Netherlands, 1996.","DOI":"10.1007\/978-1-4757-2495-0"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1007\/BF02234767"},{"key":"R15","unstructured":"Y. A. Kuznetsov,\n                      CONTENT\u2014Integrated environment for analysis of dynamical systems. Tutorial\n                      , Dynamical Systems Laboratory, Centrum voor Wiskunde en Informatica, Amsterdam, 1998, ftp.cwi.nl\/pub\/CONTENT."},{"key":"R16","unstructured":"Y. A. Kuznetsov,\n                      Elements of Applied Bifurcation Theory\n                      , 2nd ed., Springer\u2010Verlag, New York, 1998."},{"key":"R17","doi-asserted-by":"crossref","unstructured":"B. Lang,\n                      A comparison of techniques for evaluating centered forms\n                      , in Perspectives on Enclosure Methods, U. Kulisch, R. Lohner, and A. 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