连续双线性系统鞍点均衡的迭代算法  

Iterative algorithm for saddle-point equilibrium of continuous bilinear system

作　　者：朱怀念[1] 张成科[2] 武赛[1] 宾宁[1] 

机构地区：[1]广东工业大学管理学院,广州510520 [2]广东工业大学经济与贸易学院,广州510520

出　　处：《黑龙江大学自然科学学报》2010年第2期162-166,共5页Journal of Natural Science of Heilongjiang University

基　　金：国家自然科学基金资助项目(70771029);广东省自然科学基金资助项目(070117);内蒙古自治区高等学校科学技术项目(NJ09137);广东工业大学青年基金项目(082050)

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。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.

关 键 词：双线性系统 鞍点均衡 RICCATI方程 

分 类 号：O225[理学—运筹学与控制论]