Mayer型线性最优控制问题的一阶充分条件

The First Order Sufficient Conditions for Mayer Type Linear Optimal Control Problems

针对目标泛函为Mayer型的最优控制问题,在目标函数为伪凸的情形下,证明了当控制系统为线性控制时最优控制的一阶充分条件,同时证明了相应的离散最优控制问题的一阶充分条件;作为应用,通过一阶最优性条件将离散最优控制问题等价地转化为有限维变分不等式问题,并利用伪单调变分不等式的算法给出最优控制的一个数值算例。

The first order sufficient optimality condition for Mayer-type optimal control problems is established under the condition that the cost function is pseudoconvex.The control system is assumed to be linear.In addition,the first order sufficient optimality condition for the corresponding discrete optimal control problem is also proved.As an application,the discrete optimal control problem is equivalently transformed into a finite dimensional variational inequality,and a numerical example is given by the numerical algorithm for pseudo-monotone variational inequality.