@inproceedings{penedo_control_2018,
	title = {Control {Synthesis} for {Partial} {Differential} {Equations} from {Spatio}-{Temporal} {Specifications}},
	doi = {10.1109/CDC.2018.8619313},
	abstract = {In this paper, we introduce a new boundary control synthesis problem with temporal logic specifications for a wide range of linear partial differential equations. We leverage the finite element method (FEM) to reduce the problem to a control problem for discrete-time linear systems. The specifications are formalized using an extension of signal temporal logic (STL), called Spatial-STL (S-STL). A conservative procedure to reformulate the specification into a regular STL formula as part of the FEM reduction is presented. A mixed-integer linear encoding is then used to synthesize the control inputs from a given allowed set. We illustrate the algorithm by applying it to a heat propagation problem.},
	booktitle = {2018 {IEEE} {Conference} on {Decision} and {Control} ({CDC})},
	author = {Penedo, F. and Park, H. and Belta, C.},
	month = dec,
	year = {2018},
	keywords = {Mathematical model, Modeling, Trajectory, control system synthesis, discrete time systems, femformal, integer programming, temporal logic, Semantics, partial differential equations, signal temporal logic, temporal logic specifications, boundary control synthesis problem, conservative procedure, control inputs, control problem, discrete-time linear systems, FEM reduction, finite element analysis, Finite element analysis, finite element method, heat propagation problem, Heating systems, linear partial differential equations, linear programming, linear systems, mixed-integer linear encoding, Partial differential equations, regular STL formula, S-STL, Spatial-STL, spatio-temporal specifications},
	pages = {4890--4895},
	file = {IEEE Xplore Abstract Record:/home/fran/.zotero/zotero/th89c3ji.default/zotero/storage/A53TBLDA/8619313.html:text/html;IEEE Xplore Full Text PDF:/home/fran/.zotero/zotero/th89c3ji.default/zotero/storage/U6V94GZ6/Penedo et al. - 2018 - Control Synthesis for Partial Differential Equatio.pdf:application/pdf}
}