中文摘要：

研究有限时间段内的连续时不变双线性二次型性能指标的鞍点均衡问题。通过运用极大值原理，将鞍点均衡问题转化为双线性系统的非线性两点边值问题。再通过引入一个变换，将非线性两点边值问题转化成一个具有“分离”形式的“线性”两点边值问题，最后利用一种新的迭代算法对“线性”两点边值问题进行了求解，为基于双线性系统的微分博弈理论求解提供了一种新的思路。

英文摘要：

The saddle-point equilibrium for continuous bilinear-quadratic control problem in the finite time is investigated. By using the maximum principal, the saddle-point equilibrium is converted into a nonlinear two point boundary value problem. Then by using a transformation, the nonlinear two-point boundary value problem is transformed into a ＂linear＂ two-point boundary value problem with ＂separate＂ form. In the end, a new iterative algorithm is constructed to solve the problem, and which provide a new approach to solve the differential games of bilinear system.