论文标题
具有终端状态约束的确定性最佳冲动控制的价值函数的连续性
Continuity of the Value Function for Deterministic Optimal Impulse Control with Terminal State Constraint
论文作者
论文摘要
确定性的最佳冲动控制问题与终端状态约束。由于终端状态约束的出现，总体上可能是不连续的。本文的主要贡献是引入了固有条件，在该条件下值函数是连续的。然后，通过Bellman动态编程方法，得出了相应的Hamilton-Jacobi-Bellman类型的Quasi变化不平等（QVI，简称为QVI），其值函数是粘度解。仔细解决了该值函数是否表征为该QVI的唯一粘度解决方案的问题，答案是挑战性的。
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 continuous. Then by a Bellman dynamic programming method, the corresponding Hamilton-Jacobi-Bellman type quasi-variational inequality (QVI, for short) is derived for which the value function is a viscosity solution. 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.
