Optimal control problems with set-valued control and state constraints

Z. Páles, Vera Zeidan

Research output: Contribution to journalArticle

26 Citations (Scopus)

Abstract

In this paper a general optimal control problem with pure state and mixed control-state constraints is considered. These constraints are of the form of set-inclusions. Second-order necessary optimality conditions for weak local minimum are derived for this problem in terms of the original data. In particular the nonemptiness of the set of critical directions and the evaluation of its support function are expressed in terms of the given functions and set-valued maps. In order that the Lagrange multiplier corresponding to the mixed control-state inclusion constraint be represented via an integrable function, a strong normality condition involving the notion of the critical tangent cone is introduced.

Original languageEnglish
Pages (from-to)334-358
Number of pages25
JournalSIAM Journal on Optimization
Volume14
Issue number2
DOIs
Publication statusPublished - 2004

Fingerprint

Control Constraints
State Constraints
Optimal Control Problem
Inclusion
Tangent Cone
Second-order Optimality Conditions
Support Function
Set-valued Map
Pure State
Necessary Optimality Conditions
Lagrange multipliers
Local Minima
Normality
Cones
Evaluation
Form

Keywords

  • Critical cone
  • Critical tangent cone
  • First- and second-order optimality conditions
  • Set-valued constraints

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Optimal control problems with set-valued control and state constraints. / Páles, Z.; Zeidan, Vera.

In: SIAM Journal on Optimization, Vol. 14, No. 2, 2004, p. 334-358.

Research output: Contribution to journalArticle

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