一类脉冲控制最佳费用的解析表达式

A CLASS OF IMPULSE CONTROL AND THE ANALYTICAL EXPRESSION OF ITS OPTIMAL COST FUNCTION

§1.导言 脉冲控制是一种重要类型的随机控制,其实用价值及理论意义都很大,故已有很多文章对其各种模型从不同角度进行各种研究,比如[1]—[3]等.但在过去的这些研究中,或是只给了最佳控制存在的充分条件,或是证明了最佳控制的存在性。

This paper studies a class of impulse discounted cost models, proves the existance ofoptimal control and gives the analytical expression of optimal cost function. The optimal control can be constructed by reflecting the controled state for fixed me-asures on boundaries of a certain interval, the reflecting measures and interval are decided byparameters of the optimal cost function and these parameters can be obtained from computa-tion.