English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

An optimal control problem for the linear wave equation with control costchosen as the BV semi-norm in time is analyzed. This formulation enhancespiecewise constant optimal controls and penalizes the number of jumps.Existence of optimal solutions and necessary optimality conditions are derived.With numerical realisation in mind, the regularization by H1 functionals isinvestigated, and the asymptotic behavior as this regularization tends to zerois analyzed. For the H1 regularized problems the semi-smooth Newton algorithmcan be used to solve the first order optimality conditions with super-linearconvergence rate. Examples are constructed which show that the distributionalderivative of an optimal control can be a mix of absolutely continuous measureswith respect to the Lebesgue measure, a countable linear combination of Diracmeasures, and Cantor measures. Numerical results illustrate and support theanalytical results.

Optimal Control of the Linear Wave Equation by Time-Depending BV-Controls: A Semi-Smooth Newton Approach