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We study a hybrid control system in which both discrete and continuous controls are involved. The discrete controls act on the system at a given set interface. The state of the system is changed discontinuously when the trajectory hits predefined sets, namely, an autonomous jump set A or a controlled jump set C where controller can choose to jump or not. At each jump, trajectory can move to a different euclidean space. We allow the cost functionals to be unbounded with certain growth and hence the corresponding value function can be unbounded. We characterize the value function as the unique viscosity solution of the associated quasivariational inequality in a suitable function class. We also consider the evolutionary, finite horizon hybrid control problem with similar model and prove that the value function is the unique viscosity solution in the continuous function class while allowing cost functionals as well as the dynamics to be unbounded.
@article{COCV_2010__16_1_176_0,
author = {Barles, Guy and Dharmatti, Sheetal and Ramaswamy, Mythily},
title = {Unbounded viscosity solutions of hybrid control systems},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {176--193},
publisher = {EDP-Sciences},
volume = {16},
number = {1},
year = {2010},
doi = {10.1051/cocv:2008076},
mrnumber = {2598094},
zbl = {1183.49026},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2008076/}
}
TY - JOUR AU - Barles, Guy AU - Dharmatti, Sheetal AU - Ramaswamy, Mythily TI - Unbounded viscosity solutions of hybrid control systems JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2010 SP - 176 EP - 193 VL - 16 IS - 1 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/cocv:2008076/ DO - 10.1051/cocv:2008076 LA - en ID - COCV_2010__16_1_176_0 ER -
%0 Journal Article %A Barles, Guy %A Dharmatti, Sheetal %A Ramaswamy, Mythily %T Unbounded viscosity solutions of hybrid control systems %J ESAIM: Control, Optimisation and Calculus of Variations %D 2010 %P 176-193 %V 16 %N 1 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/cocv:2008076/ %R 10.1051/cocv:2008076 %G en %F COCV_2010__16_1_176_0
Barles, Guy; Dharmatti, Sheetal; Ramaswamy, Mythily. Unbounded viscosity solutions of hybrid control systems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 16 (2010) no. 1, pp. 176-193. doi: 10.1051/cocv:2008076
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