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To solve this problem efficiently, we propose a time-adaptive residual based a-posteriori error control concept based on the optimality system of this optimal control problem. This approach not only delivers an adaptive time discretization of the prediction horizon, but also suggests an adaptive time discretization of the application horizon, whose length could be either adaptive or fixed. We apply this concept for systems governed by linear parabolic PDEs and present several numerical examples which demonstrate the performance and the robustness of our adaptive MPC control concept.<\/jats:p>","DOI":"10.1007\/s10915-021-01647-0","type":"journal-article","created":{"date-parts":[[2021,11,22]],"date-time":"2021-11-22T06:02:42Z","timestamp":1637560962000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Time Adaptivity in Model Predictive Control"],"prefix":"10.1007","volume":"90","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0042-8045","authenticated-orcid":false,"given":"Alessandro","family":"Alla","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0318-0740","authenticated-orcid":false,"given":"Carmen","family":"Gr\u00e4\u00dfle","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9688-0150","authenticated-orcid":false,"given":"Michael","family":"Hinze","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2021,11,22]]},"reference":[{"key":"1647_CR1","doi-asserted-by":"publisher","DOI":"10.1002\/9781118032824","volume-title":"A Posteriori Error Estimation in Finite Element Analysis","author":"M Ainsworth","year":"2000","unstructured":"Ainsworth, M., Oden, J.T.: A Posteriori Error Estimation in Finite Element Analysis. 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