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title: "Control Synthesis for Partial Differential Equations from Spatio-Temporal Specifications"

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- Harold Park
- Calin Belta

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date: "2018-12-01"
doi: "https://doi.org/10.1109/CDC.2018.8619313"

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publication: In 2018 IEEE Conference on Decision and Control
publication_short: In CDC 2018

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.

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