On the properness of an impulsive control extension of dynamic optimization problems
Karamzin, D.Y.1, 2 ; de Oliveira, V.A.1 ; Pereira, F.L.3 ; Silva, G.N.1
1 UNESP – Universidade Estadual Paulista, Department of Applied Mathematics, São José do Rio Preto, SP, Brazil
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
ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 3, pp. 857-875.

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.

DOI : 10.1051/cocv/2014053
Classification : 49N25, 49J15
Mots-clés : Optimal control extensions, well-posedness of solutions, existence of solutions, impulsive control
Karamzin, D.Y. 1, 2 ; de Oliveira, V.A. 1 ; Pereira, F.L. 3 ; Silva, G.N. 1

1 UNESP – Universidade Estadual Paulista, Department of Applied Mathematics, São José do Rio Preto, SP, Brazil
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 
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Karamzin, D.Y.; de Oliveira, V.A.; Pereira, F.L.; Silva, G.N. On the properness of an impulsive control extension of dynamic optimization problems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 3, pp. 857-875. doi : 10.1051/cocv/2014053. http://archive.numdam.org/articles/10.1051/cocv/2014053/

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