一类二阶常微分方程最优控制函数非光滑情形的研究

The Research on the Non-smooth Circumstances of Optimal Control Function of a Kind of Second Order Ordinary Differential Equations

继续研究了一类具有状态约束的由二阶常微分方程所支配的控制问题。由状态方程的外部函数来实现系统的控制,并且控制函数属于利普希茨连续函数类。在最优控制函数非光滑的情形下,利用克拉克方向导数的概念,得到了一个最优化必要条件。

This paper further studies a kind of pointwise state constraints control problem governed by a second order ordinary differential equations.The control of the system is realized through the external function of the state equation,and the control function belongs to Lipschitz continuous function category.Under the circumstance of non-smooth optimal control function,one necessary optimality condition has been obtained by using Clarke’s concept of directional derivative.