Geodesic
Finite horizon model predictive control of electrowetting on dielectric with pinning
Harbir Antil1 ; Michael Hintermüller2 ; Ricardo H. Nochetto3 orcid ; Thomas M. Surowiec4 ; Donat Wegner5
1George Mason University, Fairfax, USA
2Weierstrass-Institute, Berlin, Germany
3University of Maryland, College Park, USA
4Philipps-Universität Marburg, Germany
5Humboldt-Universität zu Berlin, Germany
Interfaces and free boundaries, Tome 19 (2017) no. 1, pp. 1-30

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DOI

A time-discrete spatially-continuous electrowetting on dielectric (EWOD) model with contact line pinning is considered as the state system in an optimal control framework. The pinning model is based on a complementarity condition. In addition to the physical variables describing velocity, pressure, and voltage, the solid-liquid-air interface, i.e., the contact line, arises as a geometric variable that evolves in time. Due to the complementarity condition, the resulting optimal control of a free boundary problem is thus a mathematical program with equilibrium constraints (MPEC) in function space. In order to cope with the geometric variable, a finite horizon model predictive control approach is proposed. Dual stationarity conditions are derived by applying a regularization procedure, exploiting techniques from PDE-constrained optimization, and then passing to the limit in the regularization parameters. Moreover, a function-space-based numerical procedure is developed by following the theoretical limit argument used in the derivation of the dual stationarity conditions. The performance of the algorithm is demonstrated by several examples; including barycenter matching and trajectory tracking.
DOI : 10.4171/ifb/375
Classification : 49-XX, 76-XX, 90-XX
Mots-clés : Electrowetting on dielectric, EWOD, contact line pinning, surface tension, sharp interface, optimal control of free boundary problems, mathematical program with equilibrium constraints, MPEC, PDE-constrained optimization, barycenter matching, trajectory tracking

Harbir Antil  1   ; Michael Hintermüller  2   ; Ricardo H. Nochetto  3   ; Thomas M. Surowiec  4   ; Donat Wegner  5

1 George Mason University, Fairfax, USA
2 Weierstrass-Institute, Berlin, Germany
3 University of Maryland, College Park, USA
4 Philipps-Universität Marburg, Germany
5 Humboldt-Universität zu Berlin, Germany 
Harbir Antil; Michael Hintermüller; Ricardo H. Nochetto; Thomas M. Surowiec; Donat Wegner. Finite horizon model predictive control of electrowetting on dielectric with pinning. Interfaces and free boundaries, Tome 19 (2017) no. 1, pp. 1-30. doi: 10.4171/ifb/375
@article{10_4171_ifb_375,
     author = {Harbir Antil and Michael Hinterm\"uller and Ricardo H. Nochetto and Thomas M. Surowiec and Donat Wegner},
     title = {Finite horizon model predictive control of electrowetting on dielectric with pinning},
     journal = {Interfaces and free boundaries},
     pages = {1--30},
     year = {2017},
     volume = {19},
     number = {1},
     doi = {10.4171/ifb/375},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/375/}
}
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