复合型分布参数系统的一个最优控制问题

An Optimal Control Problem for Distributed Parameter System of Composed Type

考虑用二阶复合型偏微分方程所描述的分布参数系统,研究了它的一个使平方性能指标达到最小值的边界最优控制问题。在边界值问题的基础上,应用线性算子广义逆的理论,得到最优控制存在的一个充分必要条件,并提供了计算最优控制函数的一个迭代方法,还给出示例。

Consider the distributed parameter system described by the second order partial differential equation of composed type, we discuss its a boundary optimal control problem with quadratic performance. On the basis of the solution to boundary - value problems by using the theory of generolized inverses of the linear operator we obtain the necessary and sufficient condition for the existence of the optimal control. An iterative method of computing the optimal control function is provided. Finally some computational examples are also given.