[{"date_created":"2020-03-13T12:38:52Z","publisher":"Springer","title":"Feedback Control of Nonlinear PDEs Using Data-Efficient Reduced Order Models Based on the Koopman Operator","year":"2020","language":[{"iso":"eng"}],"publication":"Lecture Notes in Control and Information Sciences","abstract":[{"text":"In the development of model predictive controllers for PDE-constrained problems, the use of reduced order models is essential to enable real-time applicability. Besides local linearization approaches, proper orthogonal decomposition (POD) has been most widely used in the past in order to derive such models. Due to the huge advances concerning both theory as well as the numerical approximation, a very promising alternative based on the Koopman operator has recently emerged. In this chapter, we present two control strategies for model predictive control of nonlinear PDEs using data-efficient approximations of the Koopman operator. In the first one, the dynamic control system is replaced by a small number of autonomous systems with different yet constant inputs. The control problem is consequently transformed into a switching problem. In the second approach, a bilinear surrogate model is obtained via a convex combination of these autonomous systems. Using a recent convergence result for extended dynamic mode decomposition (EDMD), convergence of the reduced objective function can be shown. We study the properties of these two strategies with respect to solution quality, data requirements, and complexity of the resulting optimization problem using the 1-dimensional Burgers equation and the 2-dimensional Navier–Stokes equations as examples. Finally, an extension for online adaptivity is presented.","lang":"eng"}],"author":[{"first_name":"Sebastian","last_name":"Peitz","orcid":"https://orcid.org/0000-0002-3389-793X","full_name":"Peitz, Sebastian","id":"47427"},{"first_name":"Stefan","full_name":"Klus, Stefan","last_name":"Klus"}],"volume":484,"date_updated":"2022-01-06T06:52:48Z","doi":"10.1007/978-3-030-35713-9_10","publication_status":"published","publication_identifier":{"issn":["0170-8643","1610-7411"],"isbn":["9783030357122","9783030357139"]},"citation":{"mla":"Peitz, Sebastian, and Stefan Klus. “Feedback Control of Nonlinear PDEs Using Data-Efficient Reduced Order Models Based on the Koopman Operator.” <i>Lecture Notes in Control and Information Sciences</i>, vol. 484, Springer, 2020, pp. 257–82, doi:<a href=\"https://doi.org/10.1007/978-3-030-35713-9_10\">10.1007/978-3-030-35713-9_10</a>.","bibtex":"@inbook{Peitz_Klus_2020, place={Cham}, series={Lecture Notes in Control and Information Sciences}, title={Feedback Control of Nonlinear PDEs Using Data-Efficient Reduced Order Models Based on the Koopman Operator}, volume={484}, DOI={<a href=\"https://doi.org/10.1007/978-3-030-35713-9_10\">10.1007/978-3-030-35713-9_10</a>}, booktitle={Lecture Notes in Control and Information Sciences}, publisher={Springer}, author={Peitz, Sebastian and Klus, Stefan}, year={2020}, pages={257–282}, collection={Lecture Notes in Control and Information Sciences} }","short":"S. Peitz, S. Klus, in: Lecture Notes in Control and Information Sciences, Springer, Cham, 2020, pp. 257–282.","apa":"Peitz, S., &#38; Klus, S. (2020). Feedback Control of Nonlinear PDEs Using Data-Efficient Reduced Order Models Based on the Koopman Operator. In <i>Lecture Notes in Control and Information Sciences</i> (Vol. 484, pp. 257–282). Cham: Springer. <a href=\"https://doi.org/10.1007/978-3-030-35713-9_10\">https://doi.org/10.1007/978-3-030-35713-9_10</a>","ieee":"S. Peitz and S. Klus, “Feedback Control of Nonlinear PDEs Using Data-Efficient Reduced Order Models Based on the Koopman Operator,” in <i>Lecture Notes in Control and Information Sciences</i>, vol. 484, Cham: Springer, 2020, pp. 257–282.","chicago":"Peitz, Sebastian, and Stefan Klus. “Feedback Control of Nonlinear PDEs Using Data-Efficient Reduced Order Models Based on the Koopman Operator.” In <i>Lecture Notes in Control and Information Sciences</i>, 484:257–82. Lecture Notes in Control and Information Sciences. Cham: Springer, 2020. <a href=\"https://doi.org/10.1007/978-3-030-35713-9_10\">https://doi.org/10.1007/978-3-030-35713-9_10</a>.","ama":"Peitz S, Klus S. Feedback Control of Nonlinear PDEs Using Data-Efficient Reduced Order Models Based on the Koopman Operator. In: <i>Lecture Notes in Control and Information Sciences</i>. Vol 484. Lecture Notes in Control and Information Sciences. Cham: Springer; 2020:257-282. doi:<a href=\"https://doi.org/10.1007/978-3-030-35713-9_10\">10.1007/978-3-030-35713-9_10</a>"},"intvolume":"       484","page":"257-282","place":"Cham","user_id":"47427","series_title":"Lecture Notes in Control and Information Sciences","department":[{"_id":"101"}],"_id":"16289","type":"book_chapter","status":"public"},{"status":"public","type":"journal_article","article_type":"original","department":[{"_id":"101"}],"user_id":"47427","_id":"16290","project":[{"name":"Computing Resources Provided by the Paderborn Center for Parallel Computing","_id":"52"}],"page":"577–591","intvolume":"        34","citation":{"short":"K. Bieker, S. Peitz, S.L. Brunton, J.N. Kutz, M. Dellnitz, Theoretical and Computational Fluid Dynamics 34 (2020) 577–591.","bibtex":"@article{Bieker_Peitz_Brunton_Kutz_Dellnitz_2020, title={Deep model predictive flow control with limited sensor data and online learning}, volume={34}, DOI={<a href=\"https://doi.org/10.1007/s00162-020-00520-4\">10.1007/s00162-020-00520-4</a>}, journal={Theoretical and Computational Fluid Dynamics}, author={Bieker, Katharina and Peitz, Sebastian and Brunton, Steven L. and Kutz, J. Nathan and Dellnitz, Michael}, year={2020}, pages={577–591} }","mla":"Bieker, Katharina, et al. “Deep Model Predictive Flow Control with Limited Sensor Data and Online Learning.” <i>Theoretical and Computational Fluid Dynamics</i>, vol. 34, 2020, pp. 577–591, doi:<a href=\"https://doi.org/10.1007/s00162-020-00520-4\">10.1007/s00162-020-00520-4</a>.","apa":"Bieker, K., Peitz, S., Brunton, S. L., Kutz, J. N., &#38; Dellnitz, M. (2020). Deep model predictive flow control with limited sensor data and online learning. <i>Theoretical and Computational Fluid Dynamics</i>, <i>34</i>, 577–591. <a href=\"https://doi.org/10.1007/s00162-020-00520-4\">https://doi.org/10.1007/s00162-020-00520-4</a>","chicago":"Bieker, Katharina, Sebastian Peitz, Steven L. Brunton, J. Nathan Kutz, and Michael Dellnitz. “Deep Model Predictive Flow Control with Limited Sensor Data and Online Learning.” <i>Theoretical and Computational Fluid Dynamics</i> 34 (2020): 577–591. <a href=\"https://doi.org/10.1007/s00162-020-00520-4\">https://doi.org/10.1007/s00162-020-00520-4</a>.","ieee":"K. Bieker, S. Peitz, S. L. Brunton, J. N. Kutz, and M. Dellnitz, “Deep model predictive flow control with limited sensor data and online learning,” <i>Theoretical and Computational Fluid Dynamics</i>, vol. 34, pp. 577–591, 2020.","ama":"Bieker K, Peitz S, Brunton SL, Kutz JN, Dellnitz M. Deep model predictive flow control with limited sensor data and online learning. <i>Theoretical and Computational Fluid Dynamics</i>. 2020;34:577–591. doi:<a href=\"https://doi.org/10.1007/s00162-020-00520-4\">10.1007/s00162-020-00520-4</a>"},"publication_identifier":{"issn":["0935-4964","1432-2250"]},"publication_status":"published","doi":"10.1007/s00162-020-00520-4","main_file_link":[{"open_access":"1","url":"https://link.springer.com/content/pdf/10.1007/s00162-020-00520-4.pdf"}],"volume":34,"author":[{"last_name":"Bieker","id":"32829","full_name":"Bieker, Katharina","first_name":"Katharina"},{"last_name":"Peitz","orcid":"https://orcid.org/0000-0002-3389-793X","full_name":"Peitz, Sebastian","id":"47427","first_name":"Sebastian"},{"last_name":"Brunton","full_name":"Brunton, Steven L.","first_name":"Steven L."},{"last_name":"Kutz","full_name":"Kutz, J. Nathan","first_name":"J. Nathan"},{"last_name":"Dellnitz","full_name":"Dellnitz, Michael","first_name":"Michael"}],"oa":"1","date_updated":"2022-01-06T06:52:48Z","abstract":[{"lang":"eng","text":"The control of complex systems is of critical importance in many branches of science, engineering, and industry, many of which are governed by nonlinear partial differential equations. Controlling an unsteady fluid flow is particularly important, as flow control is a key enabler for technologies in energy (e.g., wind, tidal, and combustion), transportation (e.g., planes, trains, and automobiles), security (e.g., tracking airborne contamination), and health (e.g., artificial hearts and artificial respiration). However, the high-dimensional, nonlinear, and multi-scale dynamics make real-time feedback control infeasible. Fortunately, these high- dimensional systems exhibit dominant, low-dimensional patterns of activity that can be exploited for effective control in the sense that knowledge of the entire state of a system is not required. Advances in machine learning have the potential to revolutionize flow control given its ability to extract principled, low-rank feature spaces characterizing such complex systems.We present a novel deep learning modelpredictive control framework that exploits low-rank features of the flow in order to achieve considerable improvements to control performance. Instead of predicting the entire fluid state, we use a recurrent neural network (RNN) to accurately predict the control relevant quantities of the system, which are then embedded into an MPC framework to construct a feedback loop. In order to lower the data requirements and to improve the prediction accuracy and thus the control performance, incoming sensor data are used to update the RNN online. The results are validated using varying fluid flow examples of increasing complexity."}],"publication":"Theoretical and Computational Fluid Dynamics","language":[{"iso":"eng"}],"year":"2020","title":"Deep model predictive flow control with limited sensor data and online learning","date_created":"2020-03-13T12:40:09Z"},{"citation":{"ama":"Peitz S, Otto SE, Rowley CW. Data-Driven Model Predictive Control using Interpolated Koopman  Generators. <i>SIAM Journal on Applied Dynamical Systems</i>. 2020;19(3):2162-2193. doi:<a href=\"https://doi.org/10.1137/20M1325678\">10.1137/20M1325678</a>","chicago":"Peitz, Sebastian, Samuel E. Otto, and Clarence W. Rowley. “Data-Driven Model Predictive Control Using Interpolated Koopman  Generators.” <i>SIAM Journal on Applied Dynamical Systems</i> 19, no. 3 (2020): 2162–93. <a href=\"https://doi.org/10.1137/20M1325678\">https://doi.org/10.1137/20M1325678</a>.","ieee":"S. Peitz, S. E. Otto, and C. W. Rowley, “Data-Driven Model Predictive Control using Interpolated Koopman  Generators,” <i>SIAM Journal on Applied Dynamical Systems</i>, vol. 19, no. 3, pp. 2162–2193, 2020.","apa":"Peitz, S., Otto, S. E., &#38; Rowley, C. W. (2020). Data-Driven Model Predictive Control using Interpolated Koopman  Generators. <i>SIAM Journal on Applied Dynamical Systems</i>, <i>19</i>(3), 2162–2193. <a href=\"https://doi.org/10.1137/20M1325678\">https://doi.org/10.1137/20M1325678</a>","bibtex":"@article{Peitz_Otto_Rowley_2020, title={Data-Driven Model Predictive Control using Interpolated Koopman  Generators}, volume={19}, DOI={<a href=\"https://doi.org/10.1137/20M1325678\">10.1137/20M1325678</a>}, number={3}, journal={SIAM Journal on Applied Dynamical Systems}, author={Peitz, Sebastian and Otto, Samuel E. and Rowley, Clarence W.}, year={2020}, pages={2162–2193} }","short":"S. Peitz, S.E. Otto, C.W. Rowley, SIAM Journal on Applied Dynamical Systems 19 (2020) 2162–2193.","mla":"Peitz, Sebastian, et al. “Data-Driven Model Predictive Control Using Interpolated Koopman  Generators.” <i>SIAM Journal on Applied Dynamical Systems</i>, vol. 19, no. 3, 2020, pp. 2162–93, doi:<a href=\"https://doi.org/10.1137/20M1325678\">10.1137/20M1325678</a>."},"page":"2162-2193","intvolume":"        19","year":"2020","issue":"3","main_file_link":[{"url":"https://epubs.siam.org/doi/pdf/10.1137/20M1325678"}],"doi":"10.1137/20M1325678","title":"Data-Driven Model Predictive Control using Interpolated Koopman  Generators","date_created":"2020-03-17T09:53:01Z","author":[{"full_name":"Peitz, Sebastian","id":"47427","last_name":"Peitz","orcid":"0000-0002-3389-793X","first_name":"Sebastian"},{"full_name":"Otto, Samuel E.","last_name":"Otto","first_name":"Samuel E."},{"first_name":"Clarence W.","last_name":"Rowley","full_name":"Rowley, Clarence W."}],"volume":19,"date_updated":"2022-01-06T06:52:48Z","status":"public","abstract":[{"text":"In recent years, the success of the Koopman operator in dynamical systems\r\nanalysis has also fueled the development of Koopman operator-based control\r\nframeworks. In order to preserve the relatively low data requirements for an\r\napproximation via Dynamic Mode Decomposition, a quantization approach was\r\nrecently proposed in [Peitz & Klus, Automatica 106, 2019]. This way, control\r\nof nonlinear dynamical systems can be realized by means of switched systems\r\ntechniques, using only a finite set of autonomous Koopman operator-based\r\nreduced models. These individual systems can be approximated very efficiently\r\nfrom data. The main idea is to transform a control system into a set of\r\nautonomous systems for which the optimal switching sequence has to be computed.\r\nIn this article, we extend these results to continuous control inputs using\r\nrelaxation. This way, we combine the advantages of the data efficiency of\r\napproximating a finite set of autonomous systems with continuous controls. We\r\nshow that when using the Koopman generator, this relaxation --- realized by\r\nlinear interpolation between two operators --- does not introduce any error for\r\ncontrol affine systems. This allows us to control high-dimensional nonlinear\r\nsystems using bilinear, low-dimensional surrogate models. The efficiency of the\r\nproposed approach is demonstrated using several examples with increasing\r\ncomplexity, from the Duffing oscillator to the chaotic fluidic pinball.","lang":"eng"}],"type":"journal_article","publication":"SIAM Journal on Applied Dynamical Systems","language":[{"iso":"eng"}],"user_id":"47427","department":[{"_id":"101"}],"_id":"16309"},{"year":"2020","citation":{"chicago":"Hernández Castellanos, Carlos Ignacio, Sina Ober-Blöbaum, and Sebastian Peitz. “Explicit Multi-Objective Model Predictive Control for Nonlinear Systems  Under Uncertainty.” <i>International Journal of Robust and Nonlinear Control</i> 30(17) (2020): 7593–7618. <a href=\"https://doi.org/10.1002/rnc.5197\">https://doi.org/10.1002/rnc.5197</a>.","ieee":"C. I. Hernández Castellanos, S. Ober-Blöbaum, and S. Peitz, “Explicit Multi-objective Model Predictive Control for Nonlinear Systems  Under Uncertainty,” <i>International Journal of Robust and Nonlinear Control</i>, vol. 30(17), pp. 7593–7618, 2020, doi: <a href=\"https://doi.org/10.1002/rnc.5197\">10.1002/rnc.5197</a>.","ama":"Hernández Castellanos CI, Ober-Blöbaum S, Peitz S. Explicit Multi-objective Model Predictive Control for Nonlinear Systems  Under Uncertainty. <i>International Journal of Robust and Nonlinear Control</i>. 2020;30(17):7593-7618. doi:<a href=\"https://doi.org/10.1002/rnc.5197\">10.1002/rnc.5197</a>","mla":"Hernández Castellanos, Carlos Ignacio, et al. “Explicit Multi-Objective Model Predictive Control for Nonlinear Systems  Under Uncertainty.” <i>International Journal of Robust and Nonlinear Control</i>, vol. 30(17), 2020, pp. 7593–618, doi:<a href=\"https://doi.org/10.1002/rnc.5197\">10.1002/rnc.5197</a>.","short":"C.I. Hernández Castellanos, S. Ober-Blöbaum, S. Peitz, International Journal of Robust and Nonlinear Control 30(17) (2020) 7593–7618.","bibtex":"@article{Hernández Castellanos_Ober-Blöbaum_Peitz_2020, title={Explicit Multi-objective Model Predictive Control for Nonlinear Systems  Under Uncertainty}, volume={30(17)}, DOI={<a href=\"https://doi.org/10.1002/rnc.5197\">10.1002/rnc.5197</a>}, journal={International Journal of Robust and Nonlinear Control}, author={Hernández Castellanos, Carlos Ignacio and Ober-Blöbaum, Sina and Peitz, Sebastian}, year={2020}, pages={7593–7618} }","apa":"Hernández Castellanos, C. I., Ober-Blöbaum, S., &#38; Peitz, S. (2020). Explicit Multi-objective Model Predictive Control for Nonlinear Systems  Under Uncertainty. <i>International Journal of Robust and Nonlinear Control</i>, <i>30(17)</i>, 7593–7618. <a href=\"https://doi.org/10.1002/rnc.5197\">https://doi.org/10.1002/rnc.5197</a>"},"page":"7593-7618","title":"Explicit Multi-objective Model Predictive Control for Nonlinear Systems  Under Uncertainty","doi":"10.1002/rnc.5197","date_updated":"2022-01-21T09:55:39Z","date_created":"2020-03-13T12:45:56Z","author":[{"first_name":"Carlos Ignacio","full_name":"Hernández Castellanos, Carlos Ignacio","last_name":"Hernández Castellanos"},{"first_name":"Sina","id":"16494","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum"},{"first_name":"Sebastian","last_name":"Peitz","orcid":"https://orcid.org/0000-0002-3389-793X","id":"47427","full_name":"Peitz, Sebastian"}],"volume":"30(17)","abstract":[{"lang":"eng","text":"In real-world problems, uncertainties (e.g., errors in the measurement,\r\nprecision errors) often lead to poor performance of numerical algorithms when\r\nnot explicitly taken into account. This is also the case for control problems,\r\nwhere optimal solutions can degrade in quality or even become infeasible. Thus,\r\nthere is the need to design methods that can handle uncertainty. In this work,\r\nwe consider nonlinear multi-objective optimal control problems with uncertainty\r\non the initial conditions, and in particular their incorporation into a\r\nfeedback loop via model predictive control (MPC). In multi-objective optimal\r\ncontrol, an optimal compromise between multiple conflicting criteria has to be\r\nfound. For such problems, not much has been reported in terms of uncertainties.\r\nTo address this problem class, we design an offline/online framework to compute\r\nan approximation of efficient control strategies. This approach is closely\r\nrelated to explicit MPC for nonlinear systems, where the potentially expensive\r\noptimization problem is solved in an offline phase in order to enable fast\r\nsolutions in the online phase. In order to reduce the numerical cost of the\r\noffline phase, we exploit symmetries in the control problems. Furthermore, in\r\norder to ensure optimality of the solutions, we include an additional online\r\noptimization step, which is considerably cheaper than the original\r\nmulti-objective optimization problem. We test our framework on a car\r\nmaneuvering problem where safety and speed are the objectives. The\r\nmulti-objective framework allows for online adaptations of the desired\r\nobjective. Alternatively, an automatic scalarizing procedure yields very\r\nefficient feedback controls. Our results show that the method is capable of\r\ndesigning driving strategies that deal better with uncertainties in the initial\r\nconditions, which translates into potentially safer and faster driving\r\nstrategies."}],"status":"public","type":"journal_article","publication":"International Journal of Robust and Nonlinear Control","language":[{"iso":"eng"}],"_id":"16297","user_id":"15694","department":[{"_id":"101"}]},{"citation":{"ama":"Gerlach R, Ziessler A. The Approximation of Invariant Sets in Infinite Dimensional Dynamical Systems. In: Junge O, Schütze O, Ober-Blöbaum S, Padberg-Gehle K, eds. <i>Advances in Dynamics, Optimization and Computation</i>. Vol 304. Studies in Systems, Decision and Control. Springer International Publishing; 2020:66-85. doi:<a href=\"https://doi.org/10.1007/978-3-030-51264-4_3\">10.1007/978-3-030-51264-4_3</a>","chicago":"Gerlach, Raphael, and Adrian Ziessler. “The Approximation of Invariant Sets in Infinite Dimensional Dynamical Systems.” In <i>Advances in Dynamics, Optimization and Computation</i>, edited by Oliver Junge, Oliver Schütze, Sina Ober-Blöbaum, and Kathrin Padberg-Gehle, 304:66–85. Studies in Systems, Decision and Control. Cham: Springer International Publishing, 2020. <a href=\"https://doi.org/10.1007/978-3-030-51264-4_3\">https://doi.org/10.1007/978-3-030-51264-4_3</a>.","ieee":"R. Gerlach and A. Ziessler, “The Approximation of Invariant Sets in Infinite Dimensional Dynamical Systems,” in <i>Advances in Dynamics, Optimization and Computation</i>, vol. 304, O. Junge, O. Schütze, S. Ober-Blöbaum, and K. Padberg-Gehle, Eds. Cham: Springer International Publishing, 2020, pp. 66–85.","mla":"Gerlach, Raphael, and Adrian Ziessler. “The Approximation of Invariant Sets in Infinite Dimensional Dynamical Systems.” <i>Advances in Dynamics, Optimization and Computation</i>, edited by Oliver Junge et al., vol. 304, Springer International Publishing, 2020, pp. 66–85, doi:<a href=\"https://doi.org/10.1007/978-3-030-51264-4_3\">10.1007/978-3-030-51264-4_3</a>.","bibtex":"@inbook{Gerlach_Ziessler_2020, place={Cham}, series={Studies in Systems, Decision and Control}, title={The Approximation of Invariant Sets in Infinite Dimensional Dynamical Systems}, volume={304}, DOI={<a href=\"https://doi.org/10.1007/978-3-030-51264-4_3\">10.1007/978-3-030-51264-4_3</a>}, booktitle={Advances in Dynamics, Optimization and Computation}, publisher={Springer International Publishing}, author={Gerlach, Raphael and Ziessler, Adrian}, editor={Junge, Oliver and Schütze, Oliver and Ober-Blöbaum, Sina and Padberg-Gehle, Kathrin}, year={2020}, pages={66–85}, collection={Studies in Systems, Decision and Control} }","short":"R. Gerlach, A. Ziessler, in: O. Junge, O. Schütze, S. Ober-Blöbaum, K. Padberg-Gehle (Eds.), Advances in Dynamics, Optimization and Computation, Springer International Publishing, Cham, 2020, pp. 66–85.","apa":"Gerlach, R., &#38; Ziessler, A. (2020). The Approximation of Invariant Sets in Infinite Dimensional Dynamical Systems. In O. Junge, O. Schütze, S. Ober-Blöbaum, &#38; K. Padberg-Gehle (Eds.), <i>Advances in Dynamics, Optimization and Computation</i> (Vol. 304, pp. 66–85). Springer International Publishing. <a href=\"https://doi.org/10.1007/978-3-030-51264-4_3\">https://doi.org/10.1007/978-3-030-51264-4_3</a>"},"page":"66-85","intvolume":"       304","place":"Cham","publication_status":"published","publication_identifier":{"issn":["2198-4182","2198-4190"],"isbn":["9783030512637","9783030512644"]},"main_file_link":[{"url":"https://link.springer.com/chapter/10.1007/978-3-030-51264-4_3"}],"doi":"10.1007/978-3-030-51264-4_3","author":[{"first_name":"Raphael","last_name":"Gerlach","id":"32655","full_name":"Gerlach, Raphael"},{"first_name":"Adrian","full_name":"Ziessler, Adrian","last_name":"Ziessler"}],"volume":304,"date_updated":"2023-11-17T13:13:25Z","status":"public","editor":[{"full_name":"Junge, Oliver","last_name":"Junge","first_name":"Oliver"},{"last_name":"Schütze","full_name":"Schütze, Oliver","first_name":"Oliver"},{"full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","first_name":"Sina"},{"first_name":"Kathrin","full_name":"Padberg-Gehle, Kathrin","last_name":"Padberg-Gehle"}],"type":"book_chapter","user_id":"32655","series_title":"Studies in Systems, Decision and Control","department":[{"_id":"101"}],"_id":"17994","year":"2020","title":"The Approximation of Invariant Sets in Infinite Dimensional Dynamical Systems","date_created":"2020-08-14T15:02:22Z","publisher":"Springer International Publishing","abstract":[{"text":"In this work we review the novel framework for the computation of finite dimensional invariant sets of infinite dimensional dynamical systems developed in [6] and [36]. By utilizing results on embedding techniques for infinite dimensional systems we extend a classical subdivision scheme [8] as well as a continuation algorithm [7] for the computation of attractors and invariant manifolds of finite dimensional systems to the infinite dimensional case. We show how to implement this approach for the analysis of delay differential equations and partial differential equations and illustrate the feasibility of our implementation by computing the attractor of the Mackey-Glass equation and the unstable manifold of the one-dimensional Kuramoto-Sivashinsky equation.","lang":"eng"}],"publication":"Advances in Dynamics, Optimization and Computation","language":[{"iso":"eng"}]},{"_id":"16712","department":[{"_id":"101"}],"user_id":"32655","language":[{"iso":"eng"}],"publication":"Dynamical Systems","type":"journal_article","abstract":[{"text":"We investigate self-adjoint matrices A∈Rn,n with respect to their equivariance properties. We show in particular that a matrix is self-adjoint if and only if it is equivariant with respect to the action of a group Γ2(A)⊂O(n) which is isomorphic to ⊗nk=1Z2. If the self-adjoint matrix possesses multiple eigenvalues – this may, for instance, be induced by symmetry properties of an underlying dynamical system – then A is even equivariant with respect to the action of a group Γ(A)≃∏ki=1O(mi) where m1,…,mk are the multiplicities of the eigenvalues λ1,…,λk of A. We discuss implications of this result for equivariant bifurcation problems, and we briefly address further applications for the Procrustes problem, graph symmetries and Taylor expansions.","lang":"eng"}],"status":"public","date_updated":"2023-11-17T13:12:59Z","volume":35,"author":[{"last_name":"Dellnitz","full_name":"Dellnitz, Michael","first_name":"Michael"},{"id":"32643","full_name":"Gebken, Bennet","last_name":"Gebken","first_name":"Bennet"},{"id":"32655","full_name":"Gerlach, Raphael","last_name":"Gerlach","first_name":"Raphael"},{"first_name":"Stefan","full_name":"Klus, Stefan","last_name":"Klus"}],"date_created":"2020-04-16T14:07:25Z","title":"On the equivariance properties of self-adjoint matrices","doi":"10.1080/14689367.2019.1661355","main_file_link":[{"url":"https://doi.org/10.1080/14689367.2019.1661355"}],"publication_identifier":{"issn":["1468-9367","1468-9375"]},"publication_status":"published","issue":"2","year":"2020","page":"197-215","intvolume":"        35","citation":{"chicago":"Dellnitz, Michael, Bennet Gebken, Raphael Gerlach, and Stefan Klus. “On the Equivariance Properties of Self-Adjoint Matrices.” <i>Dynamical Systems</i> 35, no. 2 (2020): 197–215. <a href=\"https://doi.org/10.1080/14689367.2019.1661355\">https://doi.org/10.1080/14689367.2019.1661355</a>.","ieee":"M. Dellnitz, B. Gebken, R. Gerlach, and S. Klus, “On the equivariance properties of self-adjoint matrices,” <i>Dynamical Systems</i>, vol. 35, no. 2, pp. 197–215, 2020, doi: <a href=\"https://doi.org/10.1080/14689367.2019.1661355\">10.1080/14689367.2019.1661355</a>.","ama":"Dellnitz M, Gebken B, Gerlach R, Klus S. On the equivariance properties of self-adjoint matrices. <i>Dynamical Systems</i>. 2020;35(2):197-215. doi:<a href=\"https://doi.org/10.1080/14689367.2019.1661355\">10.1080/14689367.2019.1661355</a>","mla":"Dellnitz, Michael, et al. “On the Equivariance Properties of Self-Adjoint Matrices.” <i>Dynamical Systems</i>, vol. 35, no. 2, 2020, pp. 197–215, doi:<a href=\"https://doi.org/10.1080/14689367.2019.1661355\">10.1080/14689367.2019.1661355</a>.","short":"M. Dellnitz, B. Gebken, R. Gerlach, S. Klus, Dynamical Systems 35 (2020) 197–215.","bibtex":"@article{Dellnitz_Gebken_Gerlach_Klus_2020, title={On the equivariance properties of self-adjoint matrices}, volume={35}, DOI={<a href=\"https://doi.org/10.1080/14689367.2019.1661355\">10.1080/14689367.2019.1661355</a>}, number={2}, journal={Dynamical Systems}, author={Dellnitz, Michael and Gebken, Bennet and Gerlach, Raphael and Klus, Stefan}, year={2020}, pages={197–215} }","apa":"Dellnitz, M., Gebken, B., Gerlach, R., &#38; Klus, S. (2020). On the equivariance properties of self-adjoint matrices. <i>Dynamical Systems</i>, <i>35</i>(2), 197–215. <a href=\"https://doi.org/10.1080/14689367.2019.1661355\">https://doi.org/10.1080/14689367.2019.1661355</a>"}},{"year":"2020","page":"705-723","citation":{"apa":"Gerlach, R., Ziessler, A., Eckhardt, B., &#38; Dellnitz, M. (2020). A Set-Oriented Path Following Method for the Approximation of Parameter Dependent Attractors. <i>SIAM Journal on Applied Dynamical Systems</i>, 705–723. <a href=\"https://doi.org/10.1137/19m1247139\">https://doi.org/10.1137/19m1247139</a>","short":"R. Gerlach, A. Ziessler, B. Eckhardt, M. Dellnitz, SIAM Journal on Applied Dynamical Systems (2020) 705–723.","bibtex":"@article{Gerlach_Ziessler_Eckhardt_Dellnitz_2020, title={A Set-Oriented Path Following Method for the Approximation of Parameter Dependent Attractors}, DOI={<a href=\"https://doi.org/10.1137/19m1247139\">10.1137/19m1247139</a>}, journal={SIAM Journal on Applied Dynamical Systems}, author={Gerlach, Raphael and Ziessler, Adrian and Eckhardt, Bruno and Dellnitz, Michael}, year={2020}, pages={705–723} }","mla":"Gerlach, Raphael, et al. “A Set-Oriented Path Following Method for the Approximation of Parameter Dependent Attractors.” <i>SIAM Journal on Applied Dynamical Systems</i>, 2020, pp. 705–23, doi:<a href=\"https://doi.org/10.1137/19m1247139\">10.1137/19m1247139</a>.","ieee":"R. Gerlach, A. Ziessler, B. Eckhardt, and M. Dellnitz, “A Set-Oriented Path Following Method for the Approximation of Parameter Dependent Attractors,” <i>SIAM Journal on Applied Dynamical Systems</i>, pp. 705–723, 2020, doi: <a href=\"https://doi.org/10.1137/19m1247139\">10.1137/19m1247139</a>.","chicago":"Gerlach, Raphael, Adrian Ziessler, Bruno Eckhardt, and Michael Dellnitz. “A Set-Oriented Path Following Method for the Approximation of Parameter Dependent Attractors.” <i>SIAM Journal on Applied Dynamical Systems</i>, 2020, 705–23. <a href=\"https://doi.org/10.1137/19m1247139\">https://doi.org/10.1137/19m1247139</a>.","ama":"Gerlach R, Ziessler A, Eckhardt B, Dellnitz M. A Set-Oriented Path Following Method for the Approximation of Parameter Dependent Attractors. <i>SIAM Journal on Applied Dynamical Systems</i>. Published online 2020:705-723. doi:<a href=\"https://doi.org/10.1137/19m1247139\">10.1137/19m1247139</a>"},"publication_identifier":{"issn":["1536-0040"]},"publication_status":"published","title":"A Set-Oriented Path Following Method for the Approximation of Parameter Dependent Attractors","doi":"10.1137/19m1247139","main_file_link":[{"url":"https://epubs.siam.org/doi/epdf/10.1137/19M1247139"}],"date_updated":"2024-10-01T13:37:43Z","date_created":"2020-04-16T14:05:41Z","author":[{"first_name":"Raphael","last_name":"Gerlach","id":"32655","full_name":"Gerlach, Raphael"},{"first_name":"Adrian","last_name":"Ziessler","full_name":"Ziessler, Adrian"},{"first_name":"Bruno","full_name":"Eckhardt, Bruno","last_name":"Eckhardt"},{"first_name":"Michael","full_name":"Dellnitz, Michael","last_name":"Dellnitz"}],"abstract":[{"text":"In this work we present a set-oriented path following method for the computation of relative global\r\nattractors of parameter-dependent dynamical systems. We start with an initial approximation of the\r\nrelative global attractor for a fixed parameter λ0 computed by a set-oriented subdivision method.\r\nBy using previously obtained approximations of the parameter-dependent relative global attractor\r\nwe can track it with respect to a one-dimensional parameter λ > λ0 without restarting the whole\r\nsubdivision procedure. We illustrate the feasibility of the set-oriented path following method by\r\nexploring the dynamics in low-dimensional models for shear flows during the transition to turbulence\r\nand of large-scale atmospheric regime changes .\r\n","lang":"eng"}],"status":"public","publication":"SIAM Journal on Applied Dynamical Systems","type":"journal_article","language":[{"iso":"eng"}],"_id":"16710","department":[{"_id":"101"}],"user_id":"32655"},{"publication":"The Journal of Chemical Physics","type":"journal_article","status":"public","department":[{"_id":"101"}],"user_id":"81513","_id":"21944","language":[{"iso":"eng"}],"extern":"1","article_number":"044116","publication_identifier":{"issn":["0021-9606","1089-7690"]},"publication_status":"published","citation":{"mla":"Nüske, Feliks, et al. “Coarse-Graining Molecular Systems by Spectral Matching.” <i>The Journal of Chemical Physics</i>, 044116, 2019, doi:<a href=\"https://doi.org/10.1063/1.5100131\">10.1063/1.5100131</a>.","short":"F. Nüske, L. Boninsegna, C. Clementi, The Journal of Chemical Physics (2019).","bibtex":"@article{Nüske_Boninsegna_Clementi_2019, title={Coarse-graining molecular systems by spectral matching}, DOI={<a href=\"https://doi.org/10.1063/1.5100131\">10.1063/1.5100131</a>}, number={044116}, journal={The Journal of Chemical Physics}, author={Nüske, Feliks and Boninsegna, Lorenzo and Clementi, Cecilia}, year={2019} }","apa":"Nüske, F., Boninsegna, L., &#38; Clementi, C. (2019). Coarse-graining molecular systems by spectral matching. <i>The Journal of Chemical Physics</i>. <a href=\"https://doi.org/10.1063/1.5100131\">https://doi.org/10.1063/1.5100131</a>","ama":"Nüske F, Boninsegna L, Clementi C. Coarse-graining molecular systems by spectral matching. <i>The Journal of Chemical Physics</i>. 2019. doi:<a href=\"https://doi.org/10.1063/1.5100131\">10.1063/1.5100131</a>","chicago":"Nüske, Feliks, Lorenzo Boninsegna, and Cecilia Clementi. “Coarse-Graining Molecular Systems by Spectral Matching.” <i>The Journal of Chemical Physics</i>, 2019. <a href=\"https://doi.org/10.1063/1.5100131\">https://doi.org/10.1063/1.5100131</a>.","ieee":"F. Nüske, L. Boninsegna, and C. Clementi, “Coarse-graining molecular systems by spectral matching,” <i>The Journal of Chemical Physics</i>, 2019."},"year":"2019","date_created":"2021-04-30T17:01:13Z","author":[{"orcid":"0000-0003-2444-7889","last_name":"Nüske","full_name":"Nüske, Feliks","id":"81513","first_name":"Feliks"},{"full_name":"Boninsegna, Lorenzo","last_name":"Boninsegna","first_name":"Lorenzo"},{"first_name":"Cecilia","full_name":"Clementi, Cecilia","last_name":"Clementi"}],"date_updated":"2022-01-06T06:55:20Z","doi":"10.1063/1.5100131","title":"Coarse-graining molecular systems by spectral matching"},{"publication_status":"published","publication_identifier":{"issn":["0924-090X","1573-269X"]},"year":"2019","citation":{"ieee":"T. Sahai, A. Ziessler, S. Klus, and M. Dellnitz, “Continuous relaxations for the traveling salesman problem,” <i>Nonlinear Dynamics</i>, 2019.","chicago":"Sahai, Tuhin, Adrian Ziessler, Stefan Klus, and Michael Dellnitz. “Continuous Relaxations for the Traveling Salesman Problem.” <i>Nonlinear Dynamics</i>, 2019. <a href=\"https://doi.org/10.1007/s11071-019-05092-5\">https://doi.org/10.1007/s11071-019-05092-5</a>.","ama":"Sahai T, Ziessler A, Klus S, Dellnitz M. Continuous relaxations for the traveling salesman problem. <i>Nonlinear Dynamics</i>. 2019. doi:<a href=\"https://doi.org/10.1007/s11071-019-05092-5\">10.1007/s11071-019-05092-5</a>","bibtex":"@article{Sahai_Ziessler_Klus_Dellnitz_2019, title={Continuous relaxations for the traveling salesman problem}, DOI={<a href=\"https://doi.org/10.1007/s11071-019-05092-5\">10.1007/s11071-019-05092-5</a>}, journal={Nonlinear Dynamics}, author={Sahai, Tuhin and Ziessler, Adrian and Klus, Stefan and Dellnitz, Michael}, year={2019} }","mla":"Sahai, Tuhin, et al. “Continuous Relaxations for the Traveling Salesman Problem.” <i>Nonlinear Dynamics</i>, 2019, doi:<a href=\"https://doi.org/10.1007/s11071-019-05092-5\">10.1007/s11071-019-05092-5</a>.","short":"T. Sahai, A. Ziessler, S. Klus, M. Dellnitz, Nonlinear Dynamics (2019).","apa":"Sahai, T., Ziessler, A., Klus, S., &#38; Dellnitz, M. (2019). Continuous relaxations for the traveling salesman problem. <i>Nonlinear Dynamics</i>. <a href=\"https://doi.org/10.1007/s11071-019-05092-5\">https://doi.org/10.1007/s11071-019-05092-5</a>"},"date_updated":"2022-01-06T06:52:55Z","date_created":"2020-04-16T14:05:04Z","author":[{"first_name":"Tuhin","last_name":"Sahai","full_name":"Sahai, Tuhin"},{"first_name":"Adrian","full_name":"Ziessler, Adrian","last_name":"Ziessler"},{"first_name":"Stefan","full_name":"Klus, Stefan","last_name":"Klus"},{"first_name":"Michael","full_name":"Dellnitz, Michael","last_name":"Dellnitz"}],"title":"Continuous relaxations for the traveling salesman problem","doi":"10.1007/s11071-019-05092-5","type":"journal_article","publication":"Nonlinear Dynamics","status":"public","_id":"16709","user_id":"47427","department":[{"_id":"101"}],"language":[{"iso":"eng"}]},{"citation":{"ama":"Peitz S, Klus S. Koopman operator-based model reduction for switched-system control of PDEs. <i>Automatica</i>. 2019;106:184-191. doi:<a href=\"https://doi.org/10.1016/j.automatica.2019.05.016\">10.1016/j.automatica.2019.05.016</a>","chicago":"Peitz, Sebastian, and Stefan Klus. “Koopman Operator-Based Model Reduction for Switched-System Control of PDEs.” <i>Automatica</i> 106 (2019): 184–91. <a href=\"https://doi.org/10.1016/j.automatica.2019.05.016\">https://doi.org/10.1016/j.automatica.2019.05.016</a>.","ieee":"S. Peitz and S. Klus, “Koopman operator-based model reduction for switched-system control of PDEs,” <i>Automatica</i>, vol. 106, pp. 184–191, 2019.","apa":"Peitz, S., &#38; Klus, S. (2019). Koopman operator-based model reduction for switched-system control of PDEs. <i>Automatica</i>, <i>106</i>, 184–191. <a href=\"https://doi.org/10.1016/j.automatica.2019.05.016\">https://doi.org/10.1016/j.automatica.2019.05.016</a>","short":"S. Peitz, S. Klus, Automatica 106 (2019) 184–191.","bibtex":"@article{Peitz_Klus_2019, title={Koopman operator-based model reduction for switched-system control of PDEs}, volume={106}, DOI={<a href=\"https://doi.org/10.1016/j.automatica.2019.05.016\">10.1016/j.automatica.2019.05.016</a>}, journal={Automatica}, author={Peitz, Sebastian and Klus, Stefan}, year={2019}, pages={184–191} }","mla":"Peitz, Sebastian, and Stefan Klus. “Koopman Operator-Based Model Reduction for Switched-System Control of PDEs.” <i>Automatica</i>, vol. 106, 2019, pp. 184–91, doi:<a href=\"https://doi.org/10.1016/j.automatica.2019.05.016\">10.1016/j.automatica.2019.05.016</a>."},"intvolume":"       106","page":"184-191","year":"2019","publication_status":"published","publication_identifier":{"issn":["0005-1098"]},"doi":"10.1016/j.automatica.2019.05.016","title":"Koopman operator-based model reduction for switched-system control of PDEs","date_created":"2019-07-10T08:08:16Z","author":[{"full_name":"Peitz, Sebastian","id":"47427","orcid":"https://orcid.org/0000-0002-3389-793X","last_name":"Peitz","first_name":"Sebastian"},{"first_name":"Stefan","full_name":"Klus, Stefan","last_name":"Klus"}],"volume":106,"date_updated":"2022-01-06T06:50:46Z","status":"public","abstract":[{"text":"We present a new framework for optimal and feedback control of PDEs using Koopman operator-based reduced order models (K-ROMs). The Koopman operator is a linear but infinite-dimensional operator which describes the dynamics of observables. A numerical approximation of the Koopman operator therefore yields a linear system for the observation of an autonomous dynamical system. In our approach, by introducing a finite number of constant controls, the dynamic control system is transformed into a set of autonomous systems and the corresponding optimal control problem into a switching time optimization problem. This allows us to replace each of these systems by a K-ROM which can be solved orders of magnitude faster. By this approach, a nonlinear infinite-dimensional control problem is transformed into a low-dimensional linear problem. Using a recent convergence result for the numerical approximation via Extended Dynamic Mode Decomposition (EDMD), we show that the value of the K-ROM based objective function converges in measure to the value of the full objective function. To illustrate the results, we consider the 1D Burgers equation and the 2D Navier–Stokes equations. The numerical experiments show remarkable performance concerning both solution times and accuracy.","lang":"eng"}],"type":"journal_article","publication":"Automatica","language":[{"iso":"eng"}],"article_type":"original","user_id":"47427","department":[{"_id":"101"}],"_id":"10593"},{"date_created":"2019-07-10T08:13:31Z","title":"On the hierarchical structure of Pareto critical sets","issue":"4","year":"2019","language":[{"iso":"eng"}],"publication":"Journal of Global Optimization","abstract":[{"lang":"eng","text":"In this article we show that the boundary of the Pareto critical set of an unconstrained multiobjective optimization problem (MOP) consists of Pareto critical points of subproblems where only a subset of the set of objective functions is taken into account. If the Pareto critical set is completely described by its boundary (e.g., if we have more objective functions than dimensions in decision space), then this can be used to efficiently solve the MOP by solving a number of MOPs with fewer objective functions. If this is not the case, the results can still give insight into the structure of the Pareto critical set."}],"date_updated":"2022-01-06T06:50:46Z","author":[{"first_name":"Bennet","last_name":"Gebken","id":"32643","full_name":"Gebken, Bennet"},{"first_name":"Sebastian","id":"47427","full_name":"Peitz, Sebastian","last_name":"Peitz","orcid":"https://orcid.org/0000-0002-3389-793X"},{"first_name":"Michael","full_name":"Dellnitz, Michael","last_name":"Dellnitz"}],"volume":73,"doi":"10.1007/s10898-019-00737-6","publication_status":"published","publication_identifier":{"issn":["0925-5001","1573-2916"]},"citation":{"bibtex":"@article{Gebken_Peitz_Dellnitz_2019, title={On the hierarchical structure of Pareto critical sets}, volume={73}, DOI={<a href=\"https://doi.org/10.1007/s10898-019-00737-6\">10.1007/s10898-019-00737-6</a>}, number={4}, journal={Journal of Global Optimization}, author={Gebken, Bennet and Peitz, Sebastian and Dellnitz, Michael}, year={2019}, pages={891–913} }","mla":"Gebken, Bennet, et al. “On the Hierarchical Structure of Pareto Critical Sets.” <i>Journal of Global Optimization</i>, vol. 73, no. 4, 2019, pp. 891–913, doi:<a href=\"https://doi.org/10.1007/s10898-019-00737-6\">10.1007/s10898-019-00737-6</a>.","short":"B. Gebken, S. Peitz, M. Dellnitz, Journal of Global Optimization 73 (2019) 891–913.","apa":"Gebken, B., Peitz, S., &#38; Dellnitz, M. (2019). On the hierarchical structure of Pareto critical sets. <i>Journal of Global Optimization</i>, <i>73</i>(4), 891–913. <a href=\"https://doi.org/10.1007/s10898-019-00737-6\">https://doi.org/10.1007/s10898-019-00737-6</a>","chicago":"Gebken, Bennet, Sebastian Peitz, and Michael Dellnitz. “On the Hierarchical Structure of Pareto Critical Sets.” <i>Journal of Global Optimization</i> 73, no. 4 (2019): 891–913. <a href=\"https://doi.org/10.1007/s10898-019-00737-6\">https://doi.org/10.1007/s10898-019-00737-6</a>.","ieee":"B. Gebken, S. Peitz, and M. Dellnitz, “On the hierarchical structure of Pareto critical sets,” <i>Journal of Global Optimization</i>, vol. 73, no. 4, pp. 891–913, 2019.","ama":"Gebken B, Peitz S, Dellnitz M. On the hierarchical structure of Pareto critical sets. <i>Journal of Global Optimization</i>. 2019;73(4):891-913. doi:<a href=\"https://doi.org/10.1007/s10898-019-00737-6\">10.1007/s10898-019-00737-6</a>"},"intvolume":"        73","page":"891-913","_id":"10595","user_id":"47427","department":[{"_id":"101"}],"article_type":"original","type":"journal_article","status":"public"},{"publication_status":"published","publication_identifier":{"isbn":["9781538694145"]},"citation":{"ama":"Hanke S, Peitz S, Wallscheid O, Böcker J, Dellnitz M. Finite-Control-Set Model Predictive Control for a Permanent Magnet Synchronous Motor Application with Online Least Squares System Identification. In: <i>2019 IEEE International Symposium on Predictive Control of Electrical Drives and Power Electronics (PRECEDE)</i>. ; 2019. doi:<a href=\"https://doi.org/10.1109/precede.2019.8753313\">10.1109/precede.2019.8753313</a>","chicago":"Hanke, Soren, Sebastian Peitz, Oliver Wallscheid, Joachim Böcker, and Michael Dellnitz. “Finite-Control-Set Model Predictive Control for a Permanent Magnet Synchronous Motor Application with Online Least Squares System Identification.” In <i>2019 IEEE International Symposium on Predictive Control of Electrical Drives and Power Electronics (PRECEDE)</i>, 2019. <a href=\"https://doi.org/10.1109/precede.2019.8753313\">https://doi.org/10.1109/precede.2019.8753313</a>.","ieee":"S. Hanke, S. Peitz, O. Wallscheid, J. Böcker, and M. Dellnitz, “Finite-Control-Set Model Predictive Control for a Permanent Magnet Synchronous Motor Application with Online Least Squares System Identification,” in <i>2019 IEEE International Symposium on Predictive Control of Electrical Drives and Power Electronics (PRECEDE)</i>, 2019.","short":"S. Hanke, S. Peitz, O. Wallscheid, J. Böcker, M. Dellnitz, in: 2019 IEEE International Symposium on Predictive Control of Electrical Drives and Power Electronics (PRECEDE), 2019.","mla":"Hanke, Soren, et al. “Finite-Control-Set Model Predictive Control for a Permanent Magnet Synchronous Motor Application with Online Least Squares System Identification.” <i>2019 IEEE International Symposium on Predictive Control of Electrical Drives and Power Electronics (PRECEDE)</i>, 2019, doi:<a href=\"https://doi.org/10.1109/precede.2019.8753313\">10.1109/precede.2019.8753313</a>.","bibtex":"@inproceedings{Hanke_Peitz_Wallscheid_Böcker_Dellnitz_2019, title={Finite-Control-Set Model Predictive Control for a Permanent Magnet Synchronous Motor Application with Online Least Squares System Identification}, DOI={<a href=\"https://doi.org/10.1109/precede.2019.8753313\">10.1109/precede.2019.8753313</a>}, booktitle={2019 IEEE International Symposium on Predictive Control of Electrical Drives and Power Electronics (PRECEDE)}, author={Hanke, Soren and Peitz, Sebastian and Wallscheid, Oliver and Böcker, Joachim and Dellnitz, Michael}, year={2019} }","apa":"Hanke, S., Peitz, S., Wallscheid, O., Böcker, J., &#38; Dellnitz, M. (2019). Finite-Control-Set Model Predictive Control for a Permanent Magnet Synchronous Motor Application with Online Least Squares System Identification. In <i>2019 IEEE International Symposium on Predictive Control of Electrical Drives and Power Electronics (PRECEDE)</i>. <a href=\"https://doi.org/10.1109/precede.2019.8753313\">https://doi.org/10.1109/precede.2019.8753313</a>"},"year":"2019","author":[{"first_name":"Soren","full_name":"Hanke, Soren","last_name":"Hanke"},{"orcid":"https://orcid.org/0000-0002-3389-793X","last_name":"Peitz","full_name":"Peitz, Sebastian","id":"47427","first_name":"Sebastian"},{"first_name":"Oliver","full_name":"Wallscheid, Oliver","last_name":"Wallscheid"},{"full_name":"Böcker, Joachim","last_name":"Böcker","first_name":"Joachim"},{"first_name":"Michael","last_name":"Dellnitz","full_name":"Dellnitz, Michael"}],"date_created":"2019-07-10T08:15:23Z","date_updated":"2022-01-06T06:50:46Z","doi":"10.1109/precede.2019.8753313","title":"Finite-Control-Set Model Predictive Control for a Permanent Magnet Synchronous Motor Application with Online Least Squares System Identification","type":"conference","publication":"2019 IEEE International Symposium on Predictive Control of Electrical Drives and Power Electronics (PRECEDE)","status":"public","abstract":[{"lang":"eng","text":"In comparison to classical control approaches in the field of electrical drives like the field-oriented control (FOC), model predictive control (MPC) approaches are able to provide a higher control performance. This refers to shorter settling times, lower overshoots, and a better decoupling of control variables in case of multi-variable controls. However, this can only be achieved if the used prediction model covers the actual behavior of the plant sufficiently well. In case of model deviations, the performance utilizing MPC remains below its potential. This results in effects like increased current ripple or steady state setpoint deviations. In order to achieve a high control performance, it is therefore necessary to adapt the model to the real plant behavior. When using an online system identification, a less accurate model is sufficient for commissioning of the drive system. In this paper, the combination of a finite-control-set MPC (FCS-MPC) with a system identification is proposed. The method does not require high-frequency signal injection, but uses the measured values already required for the FCS-MPC. An evaluation of the least squares-based identification on a laboratory test bench showed that the model accuracy and thus the control performance could be improved by an online update of the prediction models."}],"user_id":"47427","department":[{"_id":"101"}],"_id":"10597","language":[{"iso":"eng"}]},{"publication":"SIAM Journal on Applied Dynamical Systems","type":"journal_article","status":"public","abstract":[{"text":" In this work we extend the novel framework developed by Dellnitz, Hessel-von Molo, and Ziessler to\r\nthe computation of finite dimensional unstable manifolds of infinite dimensional dynamical systems.\r\nTo this end, we adapt a set-oriented continuation technique developed by Dellnitz and Hohmann for\r\nthe computation of such objects of finite dimensional systems with the results obtained in the work\r\nof Dellnitz, Hessel-von Molo, and Ziessler. We show how to implement this approach for the analysis\r\nof partial differential equations and illustrate its feasibility by computing unstable manifolds of the\r\none-dimensional Kuramoto--Sivashinsky equation as well as for the Mackey--Glass delay differential\r\nequation.\r\n","lang":"eng"}],"department":[{"_id":"101"}],"user_id":"32655","_id":"16708","language":[{"iso":"eng"}],"issue":"3","publication_identifier":{"issn":["1536-0040"]},"publication_status":"published","page":"1265-1292","intvolume":"        18","citation":{"chicago":"Ziessler, Adrian, Michael Dellnitz, and Raphael Gerlach. “The Numerical Computation of Unstable Manifolds for Infinite Dimensional Dynamical Systems by Embedding Techniques.” <i>SIAM Journal on Applied Dynamical Systems</i> 18, no. 3 (2019): 1265–92. <a href=\"https://doi.org/10.1137/18m1204395\">https://doi.org/10.1137/18m1204395</a>.","ieee":"A. Ziessler, M. Dellnitz, and R. Gerlach, “The Numerical Computation of Unstable Manifolds for Infinite Dimensional Dynamical Systems by Embedding Techniques,” <i>SIAM Journal on Applied Dynamical Systems</i>, vol. 18, no. 3, pp. 1265–1292, 2019, doi: <a href=\"https://doi.org/10.1137/18m1204395\">10.1137/18m1204395</a>.","ama":"Ziessler A, Dellnitz M, Gerlach R. The Numerical Computation of Unstable Manifolds for Infinite Dimensional Dynamical Systems by Embedding Techniques. <i>SIAM Journal on Applied Dynamical Systems</i>. 2019;18(3):1265-1292. doi:<a href=\"https://doi.org/10.1137/18m1204395\">10.1137/18m1204395</a>","bibtex":"@article{Ziessler_Dellnitz_Gerlach_2019, title={The Numerical Computation of Unstable Manifolds for Infinite Dimensional Dynamical Systems by Embedding Techniques}, volume={18}, DOI={<a href=\"https://doi.org/10.1137/18m1204395\">10.1137/18m1204395</a>}, number={3}, journal={SIAM Journal on Applied Dynamical Systems}, author={Ziessler, Adrian and Dellnitz, Michael and Gerlach, Raphael}, year={2019}, pages={1265–1292} }","short":"A. Ziessler, M. Dellnitz, R. Gerlach, SIAM Journal on Applied Dynamical Systems 18 (2019) 1265–1292.","mla":"Ziessler, Adrian, et al. “The Numerical Computation of Unstable Manifolds for Infinite Dimensional Dynamical Systems by Embedding Techniques.” <i>SIAM Journal on Applied Dynamical Systems</i>, vol. 18, no. 3, 2019, pp. 1265–92, doi:<a href=\"https://doi.org/10.1137/18m1204395\">10.1137/18m1204395</a>.","apa":"Ziessler, A., Dellnitz, M., &#38; Gerlach, R. (2019). The Numerical Computation of Unstable Manifolds for Infinite Dimensional Dynamical Systems by Embedding Techniques. <i>SIAM Journal on Applied Dynamical Systems</i>, <i>18</i>(3), 1265–1292. <a href=\"https://doi.org/10.1137/18m1204395\">https://doi.org/10.1137/18m1204395</a>"},"year":"2019","volume":18,"author":[{"last_name":"Ziessler","full_name":"Ziessler, Adrian","first_name":"Adrian"},{"full_name":"Dellnitz, Michael","last_name":"Dellnitz","first_name":"Michael"},{"last_name":"Gerlach","full_name":"Gerlach, Raphael","id":"32655","first_name":"Raphael"}],"date_created":"2020-04-16T14:04:20Z","date_updated":"2023-11-17T13:13:09Z","doi":"10.1137/18m1204395","main_file_link":[{"url":"https://epubs.siam.org/doi/epdf/10.1137/18M1204395"}],"title":"The Numerical Computation of Unstable Manifolds for Infinite Dimensional Dynamical Systems by Embedding Techniques"},{"ddc":["510"],"language":[{"iso":"eng"}],"external_id":{"arxiv":["1902.08824"]},"_id":"16711","department":[{"_id":"101"}],"user_id":"32655","abstract":[{"lang":"eng","text":"Embedding techniques allow the approximations of finite dimensional\r\nattractors and manifolds of infinite dimensional dynamical systems via\r\nsubdivision and continuation methods. These approximations give a topological\r\none-to-one image of the original set. In order to additionally reveal their\r\ngeometry we use diffusion mapst o find intrinsic coordinates. We illustrate our\r\nresults on the unstable manifold of the one-dimensional Kuramoto--Sivashinsky\r\nequation, as well as for the attractor of the Mackey-Glass delay differential\r\nequation."}],"status":"public","publication":"arXiv:1902.08824","type":"preprint","title":"Revealing the intrinsic geometry of finite dimensional invariant sets of  infinite dimensional dynamical systems","main_file_link":[{"url":"https://arxiv.org/abs/1902.08824","open_access":"1"}],"oa":"1","date_updated":"2024-09-24T12:09:27Z","date_created":"2020-04-16T14:06:21Z","author":[{"full_name":"Gerlach, Raphael","id":"32655","last_name":"Gerlach","first_name":"Raphael"},{"first_name":"Péter","full_name":"Koltai, Péter","last_name":"Koltai"},{"last_name":"Dellnitz","full_name":"Dellnitz, Michael","first_name":"Michael"}],"year":"2019","citation":{"chicago":"Gerlach, Raphael, Péter Koltai, and Michael Dellnitz. “Revealing the Intrinsic Geometry of Finite Dimensional Invariant Sets of  Infinite Dimensional Dynamical Systems.” <i>ArXiv:1902.08824</i>, 2019.","ieee":"R. Gerlach, P. Koltai, and M. Dellnitz, “Revealing the intrinsic geometry of finite dimensional invariant sets of  infinite dimensional dynamical systems,” <i>arXiv:1902.08824</i>. 2019.","ama":"Gerlach R, Koltai P, Dellnitz M. Revealing the intrinsic geometry of finite dimensional invariant sets of  infinite dimensional dynamical systems. <i>arXiv:190208824</i>. Published online 2019.","bibtex":"@article{Gerlach_Koltai_Dellnitz_2019, title={Revealing the intrinsic geometry of finite dimensional invariant sets of  infinite dimensional dynamical systems}, journal={arXiv:1902.08824}, author={Gerlach, Raphael and Koltai, Péter and Dellnitz, Michael}, year={2019} }","mla":"Gerlach, Raphael, et al. “Revealing the Intrinsic Geometry of Finite Dimensional Invariant Sets of  Infinite Dimensional Dynamical Systems.” <i>ArXiv:1902.08824</i>, 2019.","short":"R. Gerlach, P. Koltai, M. Dellnitz, ArXiv:1902.08824 (2019).","apa":"Gerlach, R., Koltai, P., &#38; Dellnitz, M. (2019). Revealing the intrinsic geometry of finite dimensional invariant sets of  infinite dimensional dynamical systems. In <i>arXiv:1902.08824</i>."},"has_accepted_license":"1"},{"author":[{"first_name":"Sören","last_name":"Hanke","full_name":"Hanke, Sören"},{"last_name":"Peitz","orcid":"0000-0002-3389-793X","full_name":"Peitz, Sebastian","id":"47427","first_name":"Sebastian"},{"full_name":"Wallscheid, Oliver","last_name":"Wallscheid","first_name":"Oliver"},{"last_name":"Klus","full_name":"Klus, Stefan","first_name":"Stefan"},{"full_name":"Böcker, Joachim","last_name":"Böcker","first_name":"Joachim"},{"last_name":"Dellnitz","full_name":"Dellnitz, Michael","first_name":"Michael"}],"date_created":"2021-04-19T16:17:30Z","oa":"1","date_updated":"2022-01-06T06:55:08Z","main_file_link":[{"url":"https://arxiv.org/pdf/1804.00854.pdf","open_access":"1"}],"title":"Koopman Operator-Based Finite-Control-Set Model Predictive Control for  Electrical Drives","citation":{"ama":"Hanke S, Peitz S, Wallscheid O, Klus S, Böcker J, Dellnitz M. Koopman Operator-Based Finite-Control-Set Model Predictive Control for  Electrical Drives. <i>arXiv:180400854</i>. 2018.","chicago":"Hanke, Sören, Sebastian Peitz, Oliver Wallscheid, Stefan Klus, Joachim Böcker, and Michael Dellnitz. “Koopman Operator-Based Finite-Control-Set Model Predictive Control for  Electrical Drives.” <i>ArXiv:1804.00854</i>, 2018.","ieee":"S. Hanke, S. Peitz, O. Wallscheid, S. Klus, J. Böcker, and M. Dellnitz, “Koopman Operator-Based Finite-Control-Set Model Predictive Control for  Electrical Drives,” <i>arXiv:1804.00854</i>. 2018.","apa":"Hanke, S., Peitz, S., Wallscheid, O., Klus, S., Böcker, J., &#38; Dellnitz, M. (2018). Koopman Operator-Based Finite-Control-Set Model Predictive Control for  Electrical Drives. <i>ArXiv:1804.00854</i>.","bibtex":"@article{Hanke_Peitz_Wallscheid_Klus_Böcker_Dellnitz_2018, title={Koopman Operator-Based Finite-Control-Set Model Predictive Control for  Electrical Drives}, journal={arXiv:1804.00854}, author={Hanke, Sören and Peitz, Sebastian and Wallscheid, Oliver and Klus, Stefan and Böcker, Joachim and Dellnitz, Michael}, year={2018} }","short":"S. Hanke, S. Peitz, O. Wallscheid, S. Klus, J. Böcker, M. Dellnitz, ArXiv:1804.00854 (2018).","mla":"Hanke, Sören, et al. “Koopman Operator-Based Finite-Control-Set Model Predictive Control for  Electrical Drives.” <i>ArXiv:1804.00854</i>, 2018."},"year":"2018","user_id":"47427","department":[{"_id":"101"}],"_id":"21634","language":[{"iso":"eng"}],"type":"preprint","publication":"arXiv:1804.00854","status":"public","abstract":[{"text":"Predictive control of power electronic systems always requires a suitable\r\nmodel of the plant. Using typical physics-based white box models, a trade-off\r\nbetween model complexity (i.e. accuracy) and computational burden has to be\r\nmade. This is a challenging task with a lot of constraints, since the model\r\norder is directly linked to the number of system states. Even though white-box\r\nmodels show suitable performance in most cases, parasitic real-world effects\r\noften cannot be modeled satisfactorily with an expedient computational load.\r\nHence, a Koopman operator-based model reduction technique is presented which\r\ndirectly links the control action to the system's outputs in a black-box\r\nfashion. The Koopman operator is a linear but infinite-dimensional operator\r\ndescribing the dynamics of observables of nonlinear autonomous dynamical\r\nsystems which can be nicely applied to the switching principle of power\r\nelectronic devices. Following this data-driven approach, the model order and\r\nthe number of system states are decoupled which allows us to consider more\r\ncomplex systems. Extensive experimental tests with an automotive-type permanent\r\nmagnet synchronous motor fed by an IGBT 2-level inverter prove the feasibility\r\nof the proposed modeling technique in a finite-set model predictive control\r\napplication.","lang":"eng"}]},{"title":"Rapid Calculation of Molecular Kinetics Using Compressed Sensing","doi":"10.1021/acs.jctc.8b00089","date_updated":"2022-01-06T06:55:20Z","author":[{"last_name":"Litzinger","full_name":"Litzinger, Florian","first_name":"Florian"},{"first_name":"Lorenzo","full_name":"Boninsegna, Lorenzo","last_name":"Boninsegna"},{"full_name":"Wu, Hao","last_name":"Wu","first_name":"Hao"},{"full_name":"Nüske, Feliks","id":"81513","last_name":"Nüske","orcid":"0000-0003-2444-7889","first_name":"Feliks"},{"last_name":"Patel","full_name":"Patel, Raajen","first_name":"Raajen"},{"full_name":"Baraniuk, Richard","last_name":"Baraniuk","first_name":"Richard"},{"first_name":"Frank","full_name":"Noé, Frank","last_name":"Noé"},{"first_name":"Cecilia","full_name":"Clementi, Cecilia","last_name":"Clementi"}],"date_created":"2021-04-30T16:58:07Z","year":"2018","citation":{"apa":"Litzinger, F., Boninsegna, L., Wu, H., Nüske, F., Patel, R., Baraniuk, R., … Clementi, C. (2018). Rapid Calculation of Molecular Kinetics Using Compressed Sensing. <i>Journal of Chemical Theory and Computation</i>, 2771–2783. <a href=\"https://doi.org/10.1021/acs.jctc.8b00089\">https://doi.org/10.1021/acs.jctc.8b00089</a>","bibtex":"@article{Litzinger_Boninsegna_Wu_Nüske_Patel_Baraniuk_Noé_Clementi_2018, title={Rapid Calculation of Molecular Kinetics Using Compressed Sensing}, DOI={<a href=\"https://doi.org/10.1021/acs.jctc.8b00089\">10.1021/acs.jctc.8b00089</a>}, journal={Journal of Chemical Theory and Computation}, author={Litzinger, Florian and Boninsegna, Lorenzo and Wu, Hao and Nüske, Feliks and Patel, Raajen and Baraniuk, Richard and Noé, Frank and Clementi, Cecilia}, year={2018}, pages={2771–2783} }","short":"F. Litzinger, L. Boninsegna, H. Wu, F. Nüske, R. Patel, R. Baraniuk, F. Noé, C. Clementi, Journal of Chemical Theory and Computation (2018) 2771–2783.","mla":"Litzinger, Florian, et al. “Rapid Calculation of Molecular Kinetics Using Compressed Sensing.” <i>Journal of Chemical Theory and Computation</i>, 2018, pp. 2771–83, doi:<a href=\"https://doi.org/10.1021/acs.jctc.8b00089\">10.1021/acs.jctc.8b00089</a>.","ama":"Litzinger F, Boninsegna L, Wu H, et al. Rapid Calculation of Molecular Kinetics Using Compressed Sensing. <i>Journal of Chemical Theory and Computation</i>. 2018:2771-2783. doi:<a href=\"https://doi.org/10.1021/acs.jctc.8b00089\">10.1021/acs.jctc.8b00089</a>","chicago":"Litzinger, Florian, Lorenzo Boninsegna, Hao Wu, Feliks Nüske, Raajen Patel, Richard Baraniuk, Frank Noé, and Cecilia Clementi. “Rapid Calculation of Molecular Kinetics Using Compressed Sensing.” <i>Journal of Chemical Theory and Computation</i>, 2018, 2771–83. <a href=\"https://doi.org/10.1021/acs.jctc.8b00089\">https://doi.org/10.1021/acs.jctc.8b00089</a>.","ieee":"F. Litzinger <i>et al.</i>, “Rapid Calculation of Molecular Kinetics Using Compressed Sensing,” <i>Journal of Chemical Theory and Computation</i>, pp. 2771–2783, 2018."},"page":"2771-2783","publication_status":"published","publication_identifier":{"issn":["1549-9618","1549-9626"]},"extern":"1","language":[{"iso":"eng"}],"_id":"21940","user_id":"81513","department":[{"_id":"101"}],"status":"public","type":"journal_article","publication":"Journal of Chemical Theory and Computation"},{"year":"2018","citation":{"ama":"Klus S, Nüske F, Koltai P, et al. Data-Driven Model Reduction and Transfer Operator Approximation. <i>Journal of Nonlinear Science</i>. 2018:985-1010. doi:<a href=\"https://doi.org/10.1007/s00332-017-9437-7\">10.1007/s00332-017-9437-7</a>","ieee":"S. Klus <i>et al.</i>, “Data-Driven Model Reduction and Transfer Operator Approximation,” <i>Journal of Nonlinear Science</i>, pp. 985–1010, 2018.","chicago":"Klus, Stefan, Feliks Nüske, Péter Koltai, Hao Wu, Ioannis Kevrekidis, Christof Schütte, and Frank Noé. “Data-Driven Model Reduction and Transfer Operator Approximation.” <i>Journal of Nonlinear Science</i>, 2018, 985–1010. <a href=\"https://doi.org/10.1007/s00332-017-9437-7\">https://doi.org/10.1007/s00332-017-9437-7</a>.","bibtex":"@article{Klus_Nüske_Koltai_Wu_Kevrekidis_Schütte_Noé_2018, title={Data-Driven Model Reduction and Transfer Operator Approximation}, DOI={<a href=\"https://doi.org/10.1007/s00332-017-9437-7\">10.1007/s00332-017-9437-7</a>}, journal={Journal of Nonlinear Science}, author={Klus, Stefan and Nüske, Feliks and Koltai, Péter and Wu, Hao and Kevrekidis, Ioannis and Schütte, Christof and Noé, Frank}, year={2018}, pages={985–1010} }","mla":"Klus, Stefan, et al. “Data-Driven Model Reduction and Transfer Operator Approximation.” <i>Journal of Nonlinear Science</i>, 2018, pp. 985–1010, doi:<a href=\"https://doi.org/10.1007/s00332-017-9437-7\">10.1007/s00332-017-9437-7</a>.","short":"S. Klus, F. Nüske, P. Koltai, H. Wu, I. Kevrekidis, C. Schütte, F. Noé, Journal of Nonlinear Science (2018) 985–1010.","apa":"Klus, S., Nüske, F., Koltai, P., Wu, H., Kevrekidis, I., Schütte, C., &#38; Noé, F. (2018). Data-Driven Model Reduction and Transfer Operator Approximation. <i>Journal of Nonlinear Science</i>, 985–1010. <a href=\"https://doi.org/10.1007/s00332-017-9437-7\">https://doi.org/10.1007/s00332-017-9437-7</a>"},"page":"985-1010","publication_status":"published","publication_identifier":{"issn":["0938-8974","1432-1467"]},"title":"Data-Driven Model Reduction and Transfer Operator Approximation","doi":"10.1007/s00332-017-9437-7","date_updated":"2022-01-06T06:55:20Z","date_created":"2021-04-30T16:59:03Z","author":[{"first_name":"Stefan","full_name":"Klus, Stefan","last_name":"Klus"},{"first_name":"Feliks","orcid":"0000-0003-2444-7889","last_name":"Nüske","id":"81513","full_name":"Nüske, Feliks"},{"first_name":"Péter","full_name":"Koltai, Péter","last_name":"Koltai"},{"full_name":"Wu, Hao","last_name":"Wu","first_name":"Hao"},{"full_name":"Kevrekidis, Ioannis","last_name":"Kevrekidis","first_name":"Ioannis"},{"first_name":"Christof","last_name":"Schütte","full_name":"Schütte, Christof"},{"full_name":"Noé, Frank","last_name":"Noé","first_name":"Frank"}],"status":"public","type":"journal_article","publication":"Journal of Nonlinear Science","extern":"1","language":[{"iso":"eng"}],"_id":"21941","user_id":"81513","department":[{"_id":"101"}]},{"type":"journal_article","publication":"The Journal of Chemical Physics","status":"public","_id":"21942","user_id":"81513","department":[{"_id":"101"}],"article_number":"241723","extern":"1","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["0021-9606","1089-7690"]},"year":"2018","citation":{"apa":"Boninsegna, L., Nüske, F., &#38; Clementi, C. (2018). Sparse learning of stochastic dynamical equations. <i>The Journal of Chemical Physics</i>. <a href=\"https://doi.org/10.1063/1.5018409\">https://doi.org/10.1063/1.5018409</a>","bibtex":"@article{Boninsegna_Nüske_Clementi_2018, title={Sparse learning of stochastic dynamical equations}, DOI={<a href=\"https://doi.org/10.1063/1.5018409\">10.1063/1.5018409</a>}, number={241723}, journal={The Journal of Chemical Physics}, author={Boninsegna, Lorenzo and Nüske, Feliks and Clementi, Cecilia}, year={2018} }","mla":"Boninsegna, Lorenzo, et al. “Sparse Learning of Stochastic Dynamical Equations.” <i>The Journal of Chemical Physics</i>, 241723, 2018, doi:<a href=\"https://doi.org/10.1063/1.5018409\">10.1063/1.5018409</a>.","short":"L. Boninsegna, F. Nüske, C. Clementi, The Journal of Chemical Physics (2018).","chicago":"Boninsegna, Lorenzo, Feliks Nüske, and Cecilia Clementi. “Sparse Learning of Stochastic Dynamical Equations.” <i>The Journal of Chemical Physics</i>, 2018. <a href=\"https://doi.org/10.1063/1.5018409\">https://doi.org/10.1063/1.5018409</a>.","ieee":"L. Boninsegna, F. Nüske, and C. Clementi, “Sparse learning of stochastic dynamical equations,” <i>The Journal of Chemical Physics</i>, 2018.","ama":"Boninsegna L, Nüske F, Clementi C. Sparse learning of stochastic dynamical equations. <i>The Journal of Chemical Physics</i>. 2018. doi:<a href=\"https://doi.org/10.1063/1.5018409\">10.1063/1.5018409</a>"},"date_updated":"2022-01-06T06:55:20Z","author":[{"full_name":"Boninsegna, Lorenzo","last_name":"Boninsegna","first_name":"Lorenzo"},{"last_name":"Nüske","orcid":"0000-0003-2444-7889","full_name":"Nüske, Feliks","id":"81513","first_name":"Feliks"},{"first_name":"Cecilia","full_name":"Clementi, Cecilia","last_name":"Clementi"}],"date_created":"2021-04-30T16:59:39Z","title":"Sparse learning of stochastic dynamical equations","doi":"10.1063/1.5018409"},{"publication_status":"published","publication_identifier":{"issn":["0021-9606","1089-7690"]},"citation":{"bibtex":"@article{Hruska_Abella_Nüske_Kavraki_Clementi_2018, title={Quantitative comparison of adaptive sampling methods for protein dynamics}, DOI={<a href=\"https://doi.org/10.1063/1.5053582\">10.1063/1.5053582</a>}, number={244119}, journal={The Journal of Chemical Physics}, author={Hruska, Eugen and Abella, Jayvee R. and Nüske, Feliks and Kavraki, Lydia E. and Clementi, Cecilia}, year={2018} }","mla":"Hruska, Eugen, et al. “Quantitative Comparison of Adaptive Sampling Methods for Protein Dynamics.” <i>The Journal of Chemical Physics</i>, 244119, 2018, doi:<a href=\"https://doi.org/10.1063/1.5053582\">10.1063/1.5053582</a>.","short":"E. Hruska, J.R. Abella, F. Nüske, L.E. Kavraki, C. Clementi, The Journal of Chemical Physics (2018).","apa":"Hruska, E., Abella, J. R., Nüske, F., Kavraki, L. E., &#38; Clementi, C. (2018). Quantitative comparison of adaptive sampling methods for protein dynamics. <i>The Journal of Chemical Physics</i>. <a href=\"https://doi.org/10.1063/1.5053582\">https://doi.org/10.1063/1.5053582</a>","ama":"Hruska E, Abella JR, Nüske F, Kavraki LE, Clementi C. Quantitative comparison of adaptive sampling methods for protein dynamics. <i>The Journal of Chemical Physics</i>. 2018. doi:<a href=\"https://doi.org/10.1063/1.5053582\">10.1063/1.5053582</a>","ieee":"E. Hruska, J. R. Abella, F. Nüske, L. E. Kavraki, and C. Clementi, “Quantitative comparison of adaptive sampling methods for protein dynamics,” <i>The Journal of Chemical Physics</i>, 2018.","chicago":"Hruska, Eugen, Jayvee R. Abella, Feliks Nüske, Lydia E. Kavraki, and Cecilia Clementi. “Quantitative Comparison of Adaptive Sampling Methods for Protein Dynamics.” <i>The Journal of Chemical Physics</i>, 2018. <a href=\"https://doi.org/10.1063/1.5053582\">https://doi.org/10.1063/1.5053582</a>."},"year":"2018","author":[{"first_name":"Eugen","last_name":"Hruska","full_name":"Hruska, Eugen"},{"first_name":"Jayvee R.","full_name":"Abella, Jayvee R.","last_name":"Abella"},{"full_name":"Nüske, Feliks","id":"81513","last_name":"Nüske","orcid":"0000-0003-2444-7889","first_name":"Feliks"},{"first_name":"Lydia E.","last_name":"Kavraki","full_name":"Kavraki, Lydia E."},{"first_name":"Cecilia","last_name":"Clementi","full_name":"Clementi, Cecilia"}],"date_created":"2021-04-30T17:00:24Z","date_updated":"2022-01-06T06:55:20Z","doi":"10.1063/1.5053582","title":"Quantitative comparison of adaptive sampling methods for protein dynamics","type":"journal_article","publication":"The Journal of Chemical Physics","status":"public","user_id":"81513","department":[{"_id":"101"}],"_id":"21943","extern":"1","language":[{"iso":"eng"}],"article_number":"244119"},{"author":[{"last_name":"Gebken","full_name":"Gebken, Bennet","id":"32643","first_name":"Bennet"},{"full_name":"Peitz, Sebastian","id":"47427","last_name":"Peitz","orcid":"https://orcid.org/0000-0002-3389-793X","first_name":"Sebastian"},{"last_name":"Dellnitz","full_name":"Dellnitz, Michael","first_name":"Michael"}],"date_created":"2019-03-29T13:26:47Z","date_updated":"2022-01-06T07:04:00Z","doi":"10.1007/978-3-319-96104-0_2","conference":{"name":"NEO 2017: Numerical and Evolutionary Optimization"},"title":"A Descent Method for Equality and Inequality Constrained Multiobjective Optimization Problems","publication_identifier":{"isbn":["9783319961033","9783319961040"],"issn":["1860-949X","1860-9503"]},"publication_status":"published","citation":{"ama":"Gebken B, Peitz S, Dellnitz M. A Descent Method for Equality and Inequality Constrained Multiobjective Optimization Problems. In: <i>Numerical and Evolutionary Optimization – NEO 2017</i>. Cham; 2018. doi:<a href=\"https://doi.org/10.1007/978-3-319-96104-0_2\">10.1007/978-3-319-96104-0_2</a>","ieee":"B. Gebken, S. Peitz, and M. Dellnitz, “A Descent Method for Equality and Inequality Constrained Multiobjective Optimization Problems,” in <i>Numerical and Evolutionary Optimization – NEO 2017</i>, 2018.","chicago":"Gebken, Bennet, Sebastian Peitz, and Michael Dellnitz. “A Descent Method for Equality and Inequality Constrained Multiobjective Optimization Problems.” In <i>Numerical and Evolutionary Optimization – NEO 2017</i>. Cham, 2018. <a href=\"https://doi.org/10.1007/978-3-319-96104-0_2\">https://doi.org/10.1007/978-3-319-96104-0_2</a>.","short":"B. Gebken, S. Peitz, M. Dellnitz, in: Numerical and Evolutionary Optimization – NEO 2017, Cham, 2018.","mla":"Gebken, Bennet, et al. “A Descent Method for Equality and Inequality Constrained Multiobjective Optimization Problems.” <i>Numerical and Evolutionary Optimization – NEO 2017</i>, 2018, doi:<a href=\"https://doi.org/10.1007/978-3-319-96104-0_2\">10.1007/978-3-319-96104-0_2</a>.","bibtex":"@inproceedings{Gebken_Peitz_Dellnitz_2018, place={Cham}, title={A Descent Method for Equality and Inequality Constrained Multiobjective Optimization Problems}, DOI={<a href=\"https://doi.org/10.1007/978-3-319-96104-0_2\">10.1007/978-3-319-96104-0_2</a>}, booktitle={Numerical and Evolutionary Optimization – NEO 2017}, author={Gebken, Bennet and Peitz, Sebastian and Dellnitz, Michael}, year={2018} }","apa":"Gebken, B., Peitz, S., &#38; Dellnitz, M. (2018). A Descent Method for Equality and Inequality Constrained Multiobjective Optimization Problems. In <i>Numerical and Evolutionary Optimization – NEO 2017</i>. Cham. <a href=\"https://doi.org/10.1007/978-3-319-96104-0_2\">https://doi.org/10.1007/978-3-319-96104-0_2</a>"},"place":"Cham","year":"2018","department":[{"_id":"101"}],"user_id":"47427","_id":"8750","language":[{"iso":"eng"}],"publication":"Numerical and Evolutionary Optimization – NEO 2017","type":"conference","status":"public","abstract":[{"lang":"eng","text":"In this article we propose a descent method for equality and inequality constrained multiobjective optimization problems (MOPs) which generalizes the steepest descent method for unconstrained MOPs by Fliege and Svaiter to constrained problems by using two active set strategies. Under some regularity assumptions on the problem, we show that accumulation points of our descent method satisfy a necessary condition for local Pareto optimality. Finally, we show the typical behavior of our method in a numerical example."}]}]