{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,2]],"date-time":"2026-09-02T02:36:53Z","timestamp":1788316613266,"version":"build-2803163510"},"reference-count":25,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2009,1]]},"abstract":"<jats:p>We present a technique for computing stability and performance bounds for unconstrained nonlinear model predictive control (MPC) schemes. The technique relies on controllability properties of the system under consideration, and the computation can be formulated as an optimization problem whose complexity is independent of the state space dimension. Based on the insight obtained from the numerical solution of this problem, we derive design guidelines for nonlinear MPC schemes which guarantee stability of the closed loop for small optimization horizons. These guidelines are illustrated by a finite and an infinite dimensional example.<\/jats:p>","DOI":"10.1137\/070707853","type":"journal-article","created":{"date-parts":[[2009,3,25]],"date-time":"2009-03-25T18:04:21Z","timestamp":1238004261000},"page":"1206-1228","source":"Crossref","is-referenced-by-count":162,"title":["Analysis and Design of Unconstrained Nonlinear MPC Schemes for Finite and Infinite Dimensional Systems"],"prefix":"10.1137","volume":"48","author":[{"given":"Lars","family":"Gr\u00fcne","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2009,3,25]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","unstructured":"F. Allg\u00f6wer and A. Zheng, eds.\n                      Nonlinear model predictive control\n                      , Progress in Systems and Control Theory 26, Birkh\u00e4user Verlag, Basel, 2000.","DOI":"10.1007\/978-3-0348-8407-5"},{"key":"R2","unstructured":"E. F. Camacho and C. Bordons,\n                      Model Predictive Control\n                      , 2nd ed., Springer-Verlag, London, 2004."},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1016\/S0005-1098(98)00073-9"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2005.847055"},{"key":"R5","doi-asserted-by":"crossref","unstructured":"L. Gr\u00fcne,\n                      Computing stability and performance bounds for unconstrained NMPC schemes\n                      , in Proceedings of the 46th IEEE Conference on Decision and Control, New Orleans, LA, 2007, pp. 1263\u20131268.","DOI":"10.1109\/CDC.2007.4434156"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1016\/j.sysconle.2008.10.012"},{"key":"R7","unstructured":"L. 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