双线性系统动态博弈的鞍点均衡

The Saddle Point Equilibrium of the Dynamic Game of Bilinear System

本文从博弈论中最基础的鞍点均衡策略入手,研究双线性二次型性能指标动态博弈的鞍点均衡策略问题,通过引入一个适当的变换,将双线性系统的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,并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。

Starting from the most fundamental saddle point equilibrium strategy of game theory,this paper studies the saddle point equilibrium strategy of the dynamic game of bilinear quadratic performance index.Through an introduction of a suitable change,the problem of nonlinear two-point boundary value can be turned into a linear two-point boundary value with separated style.A new iterative algorithm has been adopted to solve the problem of linear two-point boundary value.It provides new thoughts for the solving of bilinear system-based differential game theory.