Discretization of semilinear bang-singular-bang control problems

Ursula Felgenhauer ()
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Ursula Felgenhauer: Brandenburgische Technische Universität Cottbus – Senftenberg

Computational Optimization and Applications, 2016, vol. 64, issue 1, No 11, 295-326

Abstract: Abstract 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 $$L_{1}$$ L 1 topology, the convergence is of order one w.r.t. the stepsize.

Keywords: Bang-singular control structure; Approximation of extremals; Euler method; $$L_{1}$$ L 1 error estimate; 49M25; 49M05; 49J30 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10589-015-9800-2

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