{"88e9a857661efa99f399e9d4f24b559emathematik":{"DOI":"10.1016/j.sysconle.2011.10.012","ISBN":"","ISSN":"","URL":"http://dx.doi.org/10.1016/j.sysconle.2011.10.012","abstract":"In this paper, we consider the topic of model reduction for nonlinear\n\tdynamical systems based on kernel expansions. Our approach allows\n\tfor a full offline/online decomposition and efficient online computation\n\tof the reduced model. In particular, we derive an a-posteriori state-space\n\terror estimator for the reduction error. A key ingredient is a local\n\tLipschitz constant estimation that enables rigorous a-posteriori\n\terror estimation. The computation of the error estimator is realized\n\tby solving an auxiliary differential equation during online simulations.\n\tEstimation iterations can be performed that allow a balancing between\n\testimation sharpness and computation time. 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The dynamical systems under consideration consist\n\tof a nonlinear, time- and parameter-dependent kernel expansion representing\n\tthe system's inner dynamics as well as time- and parameter-affne\n\tinputs, initial conditions and outputs. The estimators are established\n\tfor a reduction technique originally proposed in [7] and are an extension\n\tof the estimators derived in [11] to the fully time-dependent, parameterized\n\tsetting. Key features for the effcient error estimation are to use\n\tlocal Lipschitz constants provided by a certain class of kernels\n\tand an iterative scheme to balance computation cost against estimation\n\tsharpness. Together with the affnely time/parameter-dependent system\n\tcomponents a full offine/online decomposition for both the reduction\n\tprocess and the error estimators is possible. Some experimental results\n\tfor synthetic systems illustrate the effcient evaluation of the derived\n\terror estimators for different parameters.","annote":"","author":[{"family":"Wirtz","given":"Daniel"},{"family":"Haasdonk","given":"Bernard"}],"citation-label":"Wirtz2012a","collection-editor":[],"collection-title":"","container-author":[],"container-title":"Proc. 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Our approach allows\n\tfor a full offline/online decomposition and efficient online computation\n\tof the reduced model. In particular, we derive an a-posteriori state-space\n\terror estimator for the reduction error. A key ingredient is a local\n\tLipschitz constant estimation that enables rigorous a-posteriori\n\terror estimation. The computation of the error estimator is realized\n\tby solving an auxiliary differential equation during online simulations.\n\tEstimation iterations can be performed that allow a balancing between\n\testimation sharpness and computation time. Numerical experiments\n\tdemonstrate the estimation improvement over different estimator versions\n\tand the rigor and effectiveness of the error bounds.","annote":"","author":[{"family":"Wirtz","given":"Daniel"},{"family":"Haasdonk","given":"Bernard"}],"citation-label":"WH12","collection-editor":[],"collection-title":"","container-author":[],"container-title":"Systems & Control Letters","documents":[],"edition":"","editor":[],"event-date":{"date-parts":[["2012"]],"literal":"2012"},"event-place":"","id":"88e9a857661efa99f399e9d4f24b559ebritsteiner","interhash":"e80ae72fe2c1f9f79f4f7f8f5ce00735","intrahash":"88e9a857661efa99f399e9d4f24b559e","issue":"1","issued":{"date-parts":[["2012"]],"literal":"2012"},"keyword":"a-posteriori anm decomposition, dynamical error estimates, ians kernel methods, model nonlinear offline/online projection reduction, subspace systems,","misc":{"owner":"schmidta","groups":"haasdonk, haasdonk_all_papers","file":":PDF/WH12_www_preprint_error_estimation_nonlinear_kernel_based_reduced_systems.pdf:PDF","doi":"10.1016/j.sysconle.2011.10.012"},"note":"","number":"1","number-of-pages":"8","page":"203--211","page-first":"203","publisher":"Elsevier BV","publisher-place":"","status":"","title":"Efficient a-posteriori error estimation for nonlinear kernel-based reduced systems","type":"article-journal","username":"britsteiner","version":"","volume":"61"},"699c9caf6155e0598d9c980105b8118dmathematik":{"DOI":"10.1016/j.sysconle.2011.10.012","ISBN":"","ISSN":"","URL":"http://www.sciencedirect.com/science/article/pii/S0167691111002672","abstract":"In this paper, we consider the topic of model reduction for nonlinear\n\tdynamical systems based on kernel expansions. 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