《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (6): 115-121.doi: 10.6040/j.issn.1671-9352.0.2020.101
• • 上一篇
杨彩杰,孙同军*
YANG Cai-jie, SUN Tong-jun*
摘要： 讨论一维具有Neumann边界条件的抛物型最优控制问题,给出对偶状态方程和一阶最优性条件,得到最优性系统。利用“虚拟点”中心差商离散边界条件,对最优性系统建立Crank-Nicolson差分全离散格式。证明状态变量、对偶状态变量和控制变量的最大模误差估计是关于时间和空间均为二阶收敛的。最后,建立数值算例,为避免求解大型耦合代数方程组,采用迭代方法进行计算,数值结果验证理论分析结论的正确性。
中图分类号:
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