作　　者： ; ; (张成科）; (宾宁）;

机构地区： 广东工业大学管理学院

出　　处： 《系统科学与数学》 2013年第12期1391-1403,共13页

摘　　要： 研究了一类连续时间带Markov切换参数的线性二次零和随机微分博弈问题,在广义Ito微分的意义下,通过引入一个广义Riccati微分(或者代数)方程,证明了该广义Riccati方程的可解性是相应随机微分博弈问题均衡策略存在的一个充分必要条件,同时给出了最优策略闭环形式的显式解以及最优性能指标值,最后给出了数值算例验证结论的正确性. In this paper,we discuss the problem of a class of linear quadratic zerosum stochastic differential games with Markov regime switching in continuous time.Under the condition of generalized Ito's differential rule,by introducing a generalized Riccati differential(algebraic) equation,it is proved that the solvability of the associated generalized Riccati equation is both sufficient and necessary condition for the existence of equilibrium strategies,meanwhile,the explicit solution of equilibrium strategies with closed form and the optimal value of cost functional are obtained.Finally,a numerical example is given to illustrate the validity of the obtained results.

关 键 词： 随机系统 切换参数 微分博弈 广义 方程

领　　域： [电子电信] [经济管理]