具有无穷时滞的积微分方程的最优控制

Optimal Control of Integro-Differential Equations with Infinite Delay

研究了一类具有无穷时滞和瞬时脉冲的积微分方程的最优化控制问题.利用分数幂算子、相空间理论、Gronwall不等式和不动点定理得到了在空间解的存在性的充分条件,然后使用最小化序列给出了积分成本函数的最优化控制的充分条件.

The optimal control problem for a class of integro-differential equations with infinite delay and instan-taneous impulse is studied.By using fractional power operator,phase space theory,Gronwall’s inequality andfixed point theorem,the sufficient conditions for the existence of solutions in space are obtained,and then the sufficient conditions for the optimal control of the integral cost function are given by using the minimization sequence.