Continuity of the value function for deterministic optimal impulse control with terminal state constraint
Continuity of the value function for deterministic optimal impulse control with terminal state constraint
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DOI：
10.1051/cocv/2021101
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发表时间：
2020-05
期刊：
影响因子：
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通讯作者：
Yue Zhou;Xinwei Feng;J. Yong
中科院分区：
文献类型：
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作者：
Yue Zhou;Xinwei Feng;J. Yong
研究了具有终端状态约束的确定性最优脉冲控制问题。由于终端状态约束的出现，一般情况下，值函数可能是不连续的。本文的主要贡献是引入了证明值函数连续的一个内在条件。然后利用Bellman动态规划原理，推导出相应的Hamilton-Jacobi-Bellman型拟变分不等式（简称QVI）。证明了该值函数是该QVI的粘度解。价值函数是否被表征为这个QVI的唯一粘度解的问题被仔细地解决了，答案是开放的，具有挑战性。
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.