Feedback Control for Systems with Uncertain Parameters Using Online-Adaptive Reduced Models
We consider control and stabilization for large-scale dynamical systems with uncertain, time-varying parameters. The time-critical task of controlling a dynamical system poses major challenges: using large-scale models is prohibitive, and accurately inferring parameters can be expensive, too. We add...
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| Format: | Article |
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Society for Industrial & Applied Mathematics (SIAM)
2018
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| Online Access: | http://hdl.handle.net/1721.1/117043 https://orcid.org/0000-0002-3626-7925 https://orcid.org/0000-0002-5045-046X https://orcid.org/0000-0003-2156-9338 |
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| author | Kramer, Boris Peherstorfer, Benjamin Willcox, Karen E |
| author2 | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics |
| author_facet | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics Kramer, Boris Peherstorfer, Benjamin Willcox, Karen E |
| author_sort | Kramer, Boris |
| collection | MIT |
| description | We consider control and stabilization for large-scale dynamical systems with uncertain, time-varying parameters. The time-critical task of controlling a dynamical system poses major challenges: using large-scale models is prohibitive, and accurately inferring parameters can be expensive, too. We address both problems by proposing an offine-online strategy for controlling systems with time- varying parameters. During the offine phase, we use a high-fidelity model to compute a library of optimal feedback controller gains over a sampled set of parameter values. Then, during the online phase, in which the uncertain parameter changes over time, we learn a reduced-order model from system data. The learned reduced-order model is employed within an optimization routine to update the feedback control throughout the online phase. Since the system data naturally reects the uncertain parameter, the data-driven updating of the controller gains is achieved without an explicit parameter estimation step. We consider two numerical test problems in the form of partial differential equations: a convection-diffusion system, and a model for ow through a porous medium. We demonstrate on those models that the proposed method successfully stabilizes the system model in the presence of process noise. |
| first_indexed | 2024-09-23T12:36:37Z |
| format | Article |
| id | mit-1721.1/117043 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T12:36:37Z |
| publishDate | 2018 |
| publisher | Society for Industrial & Applied Mathematics (SIAM) |
| record_format | dspace |
| spelling | mit-1721.1/1170432022-10-01T10:04:38Z Feedback Control for Systems with Uncertain Parameters Using Online-Adaptive Reduced Models Kramer, Boris Peherstorfer, Benjamin Willcox, Karen E Massachusetts Institute of Technology. Department of Aeronautics and Astronautics Kramer, Boris Peherstorfer, Benjamin Willcox, Karen E We consider control and stabilization for large-scale dynamical systems with uncertain, time-varying parameters. The time-critical task of controlling a dynamical system poses major challenges: using large-scale models is prohibitive, and accurately inferring parameters can be expensive, too. We address both problems by proposing an offine-online strategy for controlling systems with time- varying parameters. During the offine phase, we use a high-fidelity model to compute a library of optimal feedback controller gains over a sampled set of parameter values. Then, during the online phase, in which the uncertain parameter changes over time, we learn a reduced-order model from system data. The learned reduced-order model is employed within an optimization routine to update the feedback control throughout the online phase. Since the system data naturally reects the uncertain parameter, the data-driven updating of the controller gains is achieved without an explicit parameter estimation step. We consider two numerical test problems in the form of partial differential equations: a convection-diffusion system, and a model for ow through a porous medium. We demonstrate on those models that the proposed method successfully stabilizes the system model in the presence of process noise. DARPA EQUiPS program (award number UTA15-001067) United States. Department of Energy. Office of Advanced Scientific Computing Research (grant DE-FG02-08ER2585) United States. Department of Energy. Office of Advanced Scientific Computing Research (grant DE-SC000929) 2018-07-23T16:56:20Z 2018-07-23T16:56:20Z 2017-08 2017-04 2018-04-17T14:41:50Z Article http://purl.org/eprint/type/JournalArticle 1536-0040 http://hdl.handle.net/1721.1/117043 Kramer, Boris, Benjamin Peherstorfer, and Karen Willcox. “Feedback Control for Systems with Uncertain Parameters Using Online-Adaptive Reduced Models.” SIAM Journal on Applied Dynamical Systems 16, no. 3 (January 2017): 1563–1586. https://orcid.org/0000-0002-3626-7925 https://orcid.org/0000-0002-5045-046X https://orcid.org/0000-0003-2156-9338 http://dx.doi.org/10.1137/16M1088958 SIAM Journal on Applied Dynamical Systems Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf Society for Industrial & Applied Mathematics (SIAM) SIAM |
| spellingShingle | Kramer, Boris Peherstorfer, Benjamin Willcox, Karen E Feedback Control for Systems with Uncertain Parameters Using Online-Adaptive Reduced Models |
| title | Feedback Control for Systems with Uncertain Parameters Using Online-Adaptive Reduced Models |
| title_full | Feedback Control for Systems with Uncertain Parameters Using Online-Adaptive Reduced Models |
| title_fullStr | Feedback Control for Systems with Uncertain Parameters Using Online-Adaptive Reduced Models |
| title_full_unstemmed | Feedback Control for Systems with Uncertain Parameters Using Online-Adaptive Reduced Models |
| title_short | Feedback Control for Systems with Uncertain Parameters Using Online-Adaptive Reduced Models |
| title_sort | feedback control for systems with uncertain parameters using online adaptive reduced models |
| url | http://hdl.handle.net/1721.1/117043 https://orcid.org/0000-0002-3626-7925 https://orcid.org/0000-0002-5045-046X https://orcid.org/0000-0003-2156-9338 |
| work_keys_str_mv | AT kramerboris feedbackcontrolforsystemswithuncertainparametersusingonlineadaptivereducedmodels AT peherstorferbenjamin feedbackcontrolforsystemswithuncertainparametersusingonlineadaptivereducedmodels AT willcoxkarene feedbackcontrolforsystemswithuncertainparametersusingonlineadaptivereducedmodels |