一类退化半线性椭圆方程的Pontryagin最大值原理

Pontryagin maximum principle for a class of degenerate semilinear elliptic system

研究一类由退化半线性椭圆方程所支配的分布参数系统的最优控制问题。由于系统的退化性,当退化点集为单点集时,利用正则化方法得到正则化方程解的一些一致估计,再通过一个逼近过程证明了非退化系统最优控制的存在性。利用变分思想,得到该分布参数系统的Pontryagin最大值原理。

The optimal control problem for distributed parameter system governed by a class of degenerate semilinear elliptic system is considered. From degeneracy of system, some uniformly estimations of solu- tion for regularizing problem are obtained by the regularization method when the set of degenerate points is a single point set. Existence of the optimal control of degenerate system is proved by a approximate ap- proach. Pontryagin maximum principle of the distributed parameter system is obtained by using variational though.