Discretization of semilinear bang-singular-bang control problems

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• 作者：Ursula Felgenhauer
• 关键词：Bang ; singular control structure ; Approximation of extremals ; Euler method ; \(L_{1}\) ; error estimate
• 刊名：Computational Optimization and Applications
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：64
• 期：1
• 页码：295-326
• 全文大小：654 KB
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• 作者单位：Ursula Felgenhauer (1)
  
  1. Institut für Angewandte Mathematik und Wissenschaftliches Rechnen, Brandenburgische Technische Universität Cottbus – Senftenberg, PF 101344, 03013, Cottbus, Germany
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Optimization
  Operations Research and Mathematical Programming
  Operation Research and Decision Theory
  Statistics
  Convex and Discrete Geometry
  
• 出版者：Springer Netherlands
• ISSN：1573-2894

文摘

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.