271 eng preprint 0 2019-05-28 2019-05-28 -- We extend the framework of sequential action control to systems of partial differential equations which can be posed as abstract linear control problems in a Hilbert space. We follow a late-lumping approach and show that the control action can be explicitly obtained from variational principles using adjoint information. Moreover, we analyze the closed-loop system obtained from the SAC feedback for quadratic stage costs. We apply this theory prototypically to an unstable heat equation and verify the results numerically. 2 Creative Commons - CC BY - Namensnennung 4.0 International Yan Brodskyi Falk Hante Arno Seidel Friedrich-Alexander-Universität Erlangen-Nürnberg Humboldt-Universität zu Berlin A03 https://opus4.kobv.de/opus4-trr154/files/271/PDE-SAC.pdf