受控系统为一类紧半群非线性发展方程的最优控制(英文)

Optimal control of systems governed by a class of nonlinear evolation equation with compact semigroup

研究无穷维空间中一类紧半群的非线性积微分方程及其对应的最优控制问题。首先 ,我们讨论对应的积分算子的紧性 ,给出此类积微分不等式相应Gronwall不等式。进而 ,证明了此类积微分方程的温和解局部和全局存在性。最后 ,给出了相应的Lagrange型最优控制存在的充分条件。

In this paper,a class of nonlinear intrgro_differential equations of infinite dimension spaces with compact semigroup and its optimal control problem is inverstigated.At first,we discuss the compactness of an associated integral.Then,local and golbal existence results of mild solutions for such a class of integro_fifferential equations are presented.Finally,sufficient conditions for existence of optimal control of Largrange problem are obtained.