Optimal unbounded control problems with affine control dependence may fail to have minimizers in the class of absolutely continuous state trajectories. For this reason, extended impulsive versions – which cannot be of measure-theoretic type – have been investigated, in which the domain is enlarged to include discontinuous state trajectories of bounded variation, and for which existence of minimizers is guaranteed. It is of interest to know whether the passage from the original optimal control problem to its extension introduces an infimum gap. This paper provides sufficient conditions for the absence of an infimum gap based on normality of extremals. In certain cases, the normality conditions reduce to simple verifiable criteria, which improve on earlier, directly-derived sufficient conditions for no infimum gap.
Accepted:
DOI: 10.1051/cocv/2018069
Keywords: Optimal control, maximum principle, impulsive control, gap phenomena
@article{COCV_2018__24_4_1645_0, author = {Motta, Monica and Rampazzo, Franco and Vinter, Richard}, title = {Normality and gap phenomena in optimal unbounded control}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {1645--1673}, publisher = {EDP-Sciences}, volume = {24}, number = {4}, year = {2018}, doi = {10.1051/cocv/2018069}, zbl = {1439.49061}, mrnumber = {3922450}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2018069/} }
TY - JOUR AU - Motta, Monica AU - Rampazzo, Franco AU - Vinter, Richard TI - Normality and gap phenomena in optimal unbounded control JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2018 SP - 1645 EP - 1673 VL - 24 IS - 4 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2018069/ DO - 10.1051/cocv/2018069 LA - en ID - COCV_2018__24_4_1645_0 ER -
%0 Journal Article %A Motta, Monica %A Rampazzo, Franco %A Vinter, Richard %T Normality and gap phenomena in optimal unbounded control %J ESAIM: Control, Optimisation and Calculus of Variations %D 2018 %P 1645-1673 %V 24 %N 4 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2018069/ %R 10.1051/cocv/2018069 %G en %F COCV_2018__24_4_1645_0
Motta, Monica; Rampazzo, Franco; Vinter, Richard. Normality and gap phenomena in optimal unbounded control. ESAIM: Control, Optimisation and Calculus of Variations, Volume 24 (2018) no. 4, pp. 1645-1673. doi : 10.1051/cocv/2018069. http://archive.numdam.org/articles/10.1051/cocv/2018069/
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