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<p>We consider a nonlinear control system with vector-valued measures as controls and with dynamics depending on time delayed states. First, we introduce a concept of discontinuous, bounded variation solution associated with this system and establish an equivalent representation formula for it, inspired by the approach known in delay-free impulsive control as the ‘graph completion’ method. Then, thanks to this equivalent formulation, we prove well-posedness properties of these solutions and also derive necessary optimality conditions in the form of a Maximum Principle for an associated optimization problem.</p>

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Optimal Control Problems with Vector-Valued Impulse Controls and Time Delays

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年9月30日

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  • Giovanni Fusco,
  • Monica Motta,
  • Richard Vinter

摘要

We consider a nonlinear control system with vector-valued measures as controls and with dynamics depending on time delayed states. First, we introduce a concept of discontinuous, bounded variation solution associated with this system and establish an equivalent representation formula for it, inspired by the approach known in delay-free impulsive control as the ‘graph completion’ method. Then, thanks to this equivalent formulation, we prove well-posedness properties of these solutions and also derive necessary optimality conditions in the form of a Maximum Principle for an associated optimization problem.