This paper concerns estimates on the distance between a trajectory of a differential inclusion and the set of feasible trajectories of the same inclusion, feasible meaning confined to a given set of constraints. We apply these estimates to investigate Lipschitz continuity of the value functions arising in optimal control, and to variational inclusions, useful for proving non degenerate necessary optimality conditions. The main feature of our analysis is the infinite dimensional framework, which can be applied to models involving PDEs.
Keywords: Semilinear differential inclusion, state constraint, neighboring feasible trajectory theorem
@article{COCV_2018__24_3_1207_0, author = {Frankowska, Helene and Marchini, Elsa M. and Mazzola, Marco}, title = {Distance estimates for state constrained trajectories of infinite dimensional differential inclusions}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {1207--1229}, publisher = {EDP-Sciences}, volume = {24}, number = {3}, year = {2018}, doi = {10.1051/cocv/2017032}, mrnumber = {3877199}, zbl = {1412.34192}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2017032/} }
TY - JOUR AU - Frankowska, Helene AU - Marchini, Elsa M. AU - Mazzola, Marco TI - Distance estimates for state constrained trajectories of infinite dimensional differential inclusions JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2018 SP - 1207 EP - 1229 VL - 24 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2017032/ DO - 10.1051/cocv/2017032 LA - en ID - COCV_2018__24_3_1207_0 ER -
%0 Journal Article %A Frankowska, Helene %A Marchini, Elsa M. %A Mazzola, Marco %T Distance estimates for state constrained trajectories of infinite dimensional differential inclusions %J ESAIM: Control, Optimisation and Calculus of Variations %D 2018 %P 1207-1229 %V 24 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2017032/ %R 10.1051/cocv/2017032 %G en %F COCV_2018__24_3_1207_0
Frankowska, Helene; Marchini, Elsa M.; Mazzola, Marco. Distance estimates for state constrained trajectories of infinite dimensional differential inclusions. ESAIM: Control, Optimisation and Calculus of Variations, Volume 24 (2018) no. 3, pp. 1207-1229. doi : 10.1051/cocv/2017032. http://archive.numdam.org/articles/10.1051/cocv/2017032/
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