Volume 21, Number 3, July-September 2015
|Page(s)||857 - 875|
|Published online||20 May 2015|
On the properness of an impulsive control extension of dynamic optimization problems
UNESP – Universidade Estadual Paulista, Department of Applied
Mathematics, São José do Rio
email@example.com, firstname.lastname@example.org & email@example.com
2 Computing Center of the Russian Academy of Sciences, Moscow, Russia
3 SYSTEC, Faculdade de Engenharia, Universidade do Porto, Rua Dr. Roberto Frias, s/n, 4200-465 Porto, Portugal
Revised: 16 June 2014
This article investigates the properness, or well-posedness, of impulsive extension of a conventional optimal control problem. This includes both well-posedness of the solution to impulsive control systems arising as result of an impulsive extension of ordinary differential systems, and existence theorems. Well-posedness in the classic Cauchy sense is proved. Approximation lemmas that guarantee sensitivity to small perturbations in control variables are obtained. Filippov type existence theorems are established. A model example is provided to show the relevance of the impulsive controls problems which are under study.
Mathematics Subject Classification: 49N25 / 49J15
Key words: Optimal control extensions / well-posedness of solutions / existence of solutions / impulsive control
© EDP Sciences, SMAI, 2015
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