Bang-bang approximation of a traveling wave
|Bang-bang approximation of a traveling wave|
|Discrete control functions:||1|
The following problem is an academic example of a PDE constrained optimal control problem with integer control constraints
and was introduced in [Hante2009]Address: Berlin, Heidelberg
Author: Hante, Falk M.; Leugering, G\"unter
Booktitle: HSCC '09: Proceedings of the 12th International Conference on Hybrid Systems: Computation and Control
Title: Optimal Boundary Control of Convention-Reaction Transport Systems with Binary Control Functions
The control task consists of choosing the boundary value of a transport equation from the extremal values of a traveling wave such that the -distance between the traveling wave and the resulting flow is minimized.
is the traveling wave (oscillating between 0 and 1), is a (small) regularization parameter and denotes the variation of over the interval . Thereby, the solution of the transport equation has to be understood in the usual weak sense defined by the characteristic equations. Systems biology
For the best known solution is given by
where denotes the indicator function of the interval .
|[Hante2009]||Hante, Falk M.; Leugering, G\"unter (2009): Optimal Boundary Control of Convention-Reaction Transport Systems with Binary Control Functions. Springer-Verlag, HSCC '09: Proceedings of the 12th International Conference on Hybrid Systems: Computation and Control|