{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T05:53:20Z","timestamp":1771998800888,"version":"3.50.1"},"reference-count":28,"publisher":"Walter de Gruyter GmbH","issue":"6","license":[{"start":{"date-parts":[[2025,5,28]],"date-time":"2025-05-28T00:00:00Z","timestamp":1748390400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,6,26]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>The model-based control of building energy systems (BES) is a hard task, since the system identification is very labor-intensive. This results in inexact models, which are subject to parameter uncertainties. Additionally, disturbances like solar radiation have a great impact on the system dynamics. In this paper we used stochastic model predictive control (SMPC) to account for parameter and disturbance uncertainties. The disturbances are modeled as time-dependent Gaussian Processes (GP), which are known as Latent-Force Models (LFM). The proposed approach is evaluated for two different BES using experimentally obtained data. The results show that the LFM-SMPC results in the lowest discomfort with a reasonable higher energy consumption compared to a constant disturbance prediction.<\/jats:p>","DOI":"10.1515\/auto-2024-0160","type":"journal-article","created":{"date-parts":[[2025,5,30]],"date-time":"2025-05-30T20:52:17Z","timestamp":1748638337000},"page":"441-450","source":"Crossref","is-referenced-by-count":1,"title":["Application of stochastic model predictive control for building energy systems using latent force models"],"prefix":"10.1515","volume":"73","author":[{"given":"Thore","family":"Wietzke","sequence":"first","affiliation":[{"name":"Chair of Automatic Control , Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg , 91058 Erlangen , Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Daniel","family":"Landgraf","sequence":"additional","affiliation":[{"name":"Chair of Automatic Control , Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg , 91058 Erlangen , Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Knut","family":"Graichen","sequence":"additional","affiliation":[{"name":"Chair of Automatic Control , Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg , 91058 Erlangen , Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2025,5,28]]},"reference":[{"key":"2025053020521306905_j_auto-2024-0160_ref_001","unstructured":"IEA, \u201cBuildings,\u201d Tech. 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Simul., vol.\u00a010, nos. 5\u20136, pp.\u00a0653\u2013671, 2017. https:\/\/doi.org\/10.1080\/19401493.2016.1243731.","DOI":"10.1080\/19401493.2016.1243731"},{"key":"2025053020521306905_j_auto-2024-0160_ref_004","doi-asserted-by":"crossref","unstructured":"P. Stoffel, L. Maier, A. K\u00fcmpel, T. Schreiber, and D. M\u00fcller, \u201cEvaluation of advanced control strategies for building energy systems,\u201d Energy Build., vol. 280, nos. 0378-7788, p. 112709, 2023. https:\/\/doi.org\/10.1016\/j.enbuild.2022.112709.","DOI":"10.1016\/j.enbuild.2022.112709"},{"key":"2025053020521306905_j_auto-2024-0160_ref_005","doi-asserted-by":"crossref","unstructured":"M. A. \u00c1lvarez, D. Luengo, and N. D. Lawrence, \u201cLinear latent force models using Gaussian processes,\u201d IEEE Trans. Pattern Anal. Mach. 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Lawrence, \u201cGaussian process latent force models for learning and stochastic control of physical systems,\u201d IEEE Trans. Autom. Control, vol.\u00a064, no.\u00a07, pp.\u00a02953\u20132960, 2019. https:\/\/doi.org\/10.1109\/tac.2018.2874749.","DOI":"10.1109\/TAC.2018.2874749"},{"key":"2025053020521306905_j_auto-2024-0160_ref_009","doi-asserted-by":"crossref","unstructured":"J. Gra\u00dfhoff, G. M\u00e4nnel, H. S. Abbas, and P. Rostalski, \u201cModel predictive control using efficient Gaussian processes for unknown disturbance inputs,\u201d in Proc. 2019 IEEE 58th Conference on Decision and Control (CDC), 2019, pp.\u00a02708\u20132713.","DOI":"10.1109\/CDC40024.2019.9030032"},{"key":"2025053020521306905_j_auto-2024-0160_ref_010","doi-asserted-by":"crossref","unstructured":"D. Landgraf, A. V\u00f6lz, and K. 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Veje, \u201cComparative analysis of white-, gray- and black-box models for thermal simulation of indoor environment: teaching building case study,\u201d in Proc. 2018 Building Performance Analysis Conference and SimBuild Co-Organized by ASHRAE and IBPSA-USA, vol. 8 of SimBuild Conference, Chicago, USA, ASHRAE\/IBPSA-USA, 2018, pp.\u00a0173\u2013180."},{"key":"2025053020521306905_j_auto-2024-0160_ref_023","doi-asserted-by":"crossref","unstructured":"J. L. Balenzategui, F. Fabero, and J. P. Silva, Solar Radiation Measurement and Solar Radiometers, Berlin Heidelberg, New York, Springer International Publishing, 2019, pp. 15\u201369.","DOI":"10.1007\/978-3-319-97484-2_2"},{"key":"2025053020521306905_j_auto-2024-0160_ref_024","doi-asserted-by":"crossref","unstructured":"C. A. Gueymard and D. R. 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