Difference between revisions of "Bang-bang approximation of a traveling wave"
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Revision as of 14:06, 16 August 2010
The following problem is an academic example of a PDE constrained optimal control problem with integer control constraints.
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.
Mathematical formulation
where
is the traveling wave (oscillating between 0 and 1), is a (small) regularization parameter and denotes the variation of q(\cdot) over the interval . Thereby, the solution of the transport equation has to be understood in the usual weak sense defined by the characteristic equations.
References
<bibreferences/>