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.

Keywords: Optimal control extensions, well-posedness of solutions, existence of solutions, impulsive control

^{1, 2}; de Oliveira, V.A.

^{1}; Pereira, F.L.

^{3}; Silva, G.N.

^{1}

@article{COCV_2015__21_3_857_0, author = {Karamzin, D.Y. and de Oliveira, V.A. and Pereira, F.L. and Silva, G.N.}, title = {On the properness of an impulsive control extension of dynamic optimization problems}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {857--875}, publisher = {EDP-Sciences}, volume = {21}, number = {3}, year = {2015}, doi = {10.1051/cocv/2014053}, mrnumber = {3358633}, zbl = {1318.49068}, language = {en}, url = {http://www.numdam.org/articles/10.1051/cocv/2014053/} }

TY - JOUR AU - Karamzin, D.Y. AU - de Oliveira, V.A. AU - Pereira, F.L. AU - Silva, G.N. TI - On the properness of an impulsive control extension of dynamic optimization problems JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2015 SP - 857 EP - 875 VL - 21 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2014053/ DO - 10.1051/cocv/2014053 LA - en ID - COCV_2015__21_3_857_0 ER -

%0 Journal Article %A Karamzin, D.Y. %A de Oliveira, V.A. %A Pereira, F.L. %A Silva, G.N. %T On the properness of an impulsive control extension of dynamic optimization problems %J ESAIM: Control, Optimisation and Calculus of Variations %D 2015 %P 857-875 %V 21 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2014053/ %R 10.1051/cocv/2014053 %G en %F COCV_2015__21_3_857_0

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, Volume 21 (2015) no. 3, pp. 857-875. doi : 10.1051/cocv/2014053. http://www.numdam.org/articles/10.1051/cocv/2014053/

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