Discretization of semilinear bang-singular-bang control problems

  • Ursula Felgenhauer


Bang-singular controls may appear in optimal control problems where the control enters the system linearly. We analyze a discretization of the first-order system of necessary optimality conditions written in terms of a variational inequality (or: inclusion) under appropriate assumptions including second-order optimality conditions. For the so-called semilinear case, it is proved that the discrete control has the same principal bang-singular-bang structure as the reference control and, in \(L_{1}\) topology, the convergence is of order one w.r.t. the stepsize.


Bang-singular control structure Approximation of extremals Euler method \(L_{1}\) error estimate 

Mathematics Subject Classification

49M25 49M05 49J30 



The author is grateful to the anonymous referees for their instructive comments which, in particular, helped to close a gap in one of the main proofs.


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Institut für Angewandte Mathematik und Wissenschaftliches RechnenBrandenburgische Technische Universität Cottbus – SenftenbergCottbusGermany

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