Banach空间中线性发展方程的初值最优控制问题

The Initial Optimal Control for the Linear Evolution Equation in Banach Space X

本文讨论一般 Banach 空间X上发展方程(?)+Ay(t)=0,y(O)=v的初值最优控制问题。通过引入控制函数空间的方法,证明了最优控制的存在性,并给出刻划最优控制的优化系统。本文是[1]Lions.J.L.的结果的一个推广,那里要假定 Banach 空间X是自反的,甚至是 Hilbert 空间。

The problem of the initial optimal contol for the linear evolution equationwas discussed.Following the introducing control function space method asgiven in(1),the existence of the optimal control was proved and the optima-lity was given.This partly generalized a result of Lions.J.L(1),where thestate space X was assumed to be reflexive,even more Hilbert space.