Bang-bang and multiple valued optimal solutions of control problems related to quasi-linear elliptic equations

Behrouz Emamizadeh, Yichen Liu

Research output: Journal PublicationArticlepeer-review

Abstract

This paper investigates two optimal control problems in which the state equation is a quasi-linear elliptic partial differential equation. In the first problem the admissible set comprises functions with range in the interval [0, 1] with prescribed integral. We show the optimal solution is unique and it is of bang-bang type. In the second problem the admissible set is a particular class of simple functions. We will show again the optimal solution is unique and derive the corresponding optimality condition.

Original languageEnglish
Pages (from-to)1103-1117
Number of pages15
JournalSIAM Journal on Control and Optimization
Volume58
Issue number2
DOIs
Publication statusPublished - 2020

Keywords

  • Existence
  • Optimal control
  • Optimality conditions
  • Quasi-linear elliptic equations
  • Uniqueness

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics

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