带脉冲模的广义线性系统的二次最优控制

THE QUADRATIC OPTIMUM CONTROL FOR SINGULAR LINEAR SYSTEMS WITH IMPULSE MODE

<正> 广义线性系统的二次最优控制问题是人们普遍关注的研究课题.虽有不少讨论,但都有不尽人意之处.例如,有人先将广义系统正常化后再讨论其最优控制,这样就回到了正常线性系统的已知结果;有人把一部分状态作为控制变量来求解,因此,这种控制方式实际上是不能实现的.在[1]中,我们曾讨论过无脉冲模的广义线性系统二次最优控制问题,给出了(x~*,u~*)为最优解的充要条件.由于没有涉及到脉冲模的存在。

In this paper the quadratic optimum control for singular linear systems with impulsemode is discussed by using the functional analysis method.The necessary and sufficient condi-tions for the problem to be solvable are obtained.The results indicate that there does not exista quadratic optimum control of state feedback form for singular linear systems with impulsemode.