奇异双线性系统二次型微分博弈的鞍点均衡

摘要

This paper investigates the saddle-point equilibrium of quadratic differential game for singular bilinear systems in the finite time. As it is complex to solve the problem, a reduced-order transformation is introduced in order to obtain the fast and slow subsystems, then, the optimal control is obtained by using the maximum principle.In the end, the simulation of a numerical example is presented to illustrate the correctness and effectiveness of the proposed algorithm.%研究了有限时间段内的奇异双线性二次型性能指标的鞍点均衡问题.针对问题求解的复杂性,引入降阶变换将问题分解为快、慢两个子系统,然后利用极大值原理求得了系统的最优控制策略.最后给出了数值算例的仿真以验证算法的正确性和有效性.