Deterministic optimal impulse control problem with terminal state constraint is considered. Due to the appearance of the terminal state constraint, the value function might be discontinuous in general. The main contribution of this paper is the introduction of an intrinsic condition under which the value function is proved to be continuous. Then by a Bellman dynamic programming principle, the corresponding Hamilton-Jacobi-Bellman type quasi-variational inequality (QVI, for short) is derived. The value function is proved to be a viscosity solution to such a QVI. The issue of whether the value function is characterized as the unique viscosity solution to this QVI is carefully addressed and the answer is left open challengingly.
Keywords: Optimal impulse control, terminal state constraint, continuity of value function, Hamilton-Jacobi-Bellman quasi-variational inequality, viscosity solution
@article{COCV_2021__27_1_A106_0,
author = {Zhou, Yue and Feng, Xinwei and Yong, Jiongmin},
title = {Continuity of the value function for deterministic optimal impulse control with terminal state constraint},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
year = {2021},
publisher = {EDP-Sciences},
volume = {27},
doi = {10.1051/cocv/2021101},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2021101/}
}
TY - JOUR AU - Zhou, Yue AU - Feng, Xinwei AU - Yong, Jiongmin TI - Continuity of the value function for deterministic optimal impulse control with terminal state constraint JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2021 VL - 27 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2021101/ DO - 10.1051/cocv/2021101 LA - en ID - COCV_2021__27_1_A106_0 ER -
%0 Journal Article %A Zhou, Yue %A Feng, Xinwei %A Yong, Jiongmin %T Continuity of the value function for deterministic optimal impulse control with terminal state constraint %J ESAIM: Control, Optimisation and Calculus of Variations %D 2021 %V 27 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/cocv/2021101/ %R 10.1051/cocv/2021101 %G en %F COCV_2021__27_1_A106_0
Zhou, Yue; Feng, Xinwei; Yong, Jiongmin. Continuity of the value function for deterministic optimal impulse control with terminal state constraint. ESAIM: Control, Optimisation and Calculus of Variations, Tome 27 (2021), article no. 104. doi: 10.1051/cocv/2021101
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