【作者】 周中成；

【Author】 Zhou Zhongcheng 1.Key Laboratory of Systems and Control,CAS,Beijing 100190,P.R.China 2.School of Mathematics and Statistics,Southwest University,Chongqing 400715,P.R.China

【机构】 中国科学院系统控制重点实验室； 西南大学数学与统计学院；

【摘要】 本文采用最优控制办法导出了线性椭圆方程的Lyapunov不等式,即文献[4]中的重要结果,同时还获得了一些新的结果。在超临界情形下,我们通过最优控制的必要条件,得到了最优控制系统的解空间是一维的,同时给出了最优反馈控制正好就是文献[4]中定理1的结果;在临界的情形下,我们不能得到最优反馈控制,但可以获得最优控制的Pontragin最大值原理。更多还原

【Abstract】 This paper is devoted to establishing the Lyapunov inequality for PDE by means of an optimal control approach,via which we obtain the important results in paper [4],and some new results in this direction.In the supercritical case,through the necessary condition of the optimal control pair,we show that the solution space of the optimal control equation is 1-d,by which we obtain the optimal feedback control coinciding with the result of theorem 1;In the critical case,instead of the optimal feedback control,we show Pontragin’s Maximum Principle for the optimal control pair,which is the necessary condition for the optimal control pair.更多还原