OPTIMAL CONTROL OF TRANSVERSE VIBRATION OF A MOVING STRING WITH TIME-VARYING LENGTHS

Bing Sun*

*Corresponding author for this work

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Abstract

In this article, we are concerned with optimal control for the transverse vibration of a moving string with time-varying lengths. In the fixed final time horizon case, the Pontryagin maximum principle is established for the investigational system with a moving boundary, owing to the Dubovitskii and Milyutin functional analytical approach. A remark then follows for discussing the utilization of obtained necessary optimality condition.

Original languageEnglish
Pages (from-to)733-746
Number of pages14
JournalMathematical Control and Related Fields
Volume12
Issue number3
DOIs
Publication statusPublished - Sept 2022

Keywords

  • Optimal control
  • maximum principle
  • moving boundary
  • necessary optimality condition
  • time-varying length
  • transverse vibration

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Sun, B. (2022). OPTIMAL CONTROL OF TRANSVERSE VIBRATION OF A MOVING STRING WITH TIME-VARYING LENGTHS. Mathematical Control and Related Fields, 12(3), 733-746. https://doi.org/10.3934/mcrf.2021042