基于最优控制的微分博弈问题研究

发布时间：2018-03-26 03:18

本文选题：二人微分博弈　切入点：鞍点均衡　出处：《云南师范大学》2015年硕士论文

【摘要】：近年来,二人微分博弈成为最优控制领域的研究重点之一,随着最优控制研究方法的加入,推动了博弈论研究的新高潮,在此背景下,本文借助最优控制的研究方法,分类研究了不同情况下的二人博弈问题,即:一种是确定性情况下的非自治二人零和微分博弈;另一种是随机线性非二次二人零和微分博弈。本文主要分为四部分:首先,笔者介绍了一下本文的选题背景和研究进展;其次,对于确定性情况下的非自治二人零和微分博弈问题,主要是通过运用极大极小值原理来给出其最优控制策略的显示表达式,并将其和拟黎卡提微分方程的解相结合,从而推出两者之间的关系,为研究随机线性二人零和微分博弈问题做铺垫;然后,对于随机情况下的线性非二次二人零和微分博弈问题,主要是通过引进拟黎卡提微分方程,证明了拟黎卡提微分方程的可解性是相应的随机线性非二次二人零和微分博弈的鞍点策略存在的充分条件,并给出了最优控制策略的显示表达式和最优性能指标函数值;最后,总结和展望,在总结全文内容的基础上,对随机线性二人零和微分博弈的未来研究方向进行了论述。
[Abstract]:In recent years, the two-person differential game has become one of the key points in the field of optimal control. With the addition of the optimal control research method, the research of game theory has been promoted to a new climax. Under this background, this paper makes use of the research method of optimal control. This paper studies the problem of two-person game in different cases, that is, one is a non-autonomous two-person zero-sum differential game under deterministic conditions, the other is a stochastic linear non-quadratic two-person zero-sum differential game. This paper is divided into four parts: first, The author introduces the background and research progress of this paper. Secondly, for the non-autonomous two-person zero-sum differential game under deterministic conditions, the display expression of its optimal control strategy is given by using the minimax principle. By combining it with the solution of quasi Riccati differential equation, the relationship between them can be deduced, which will pave the way for studying the problem of stochastic linear two-person zero-sum differential game. For the problem of linear non-quadratic two-person zero-sum differential game under random conditions, the quasi Riccati differential equation is introduced. It is proved that the solvability of quasi Riccati differential equation is a sufficient condition for the existence of saddle point strategy of the stochastic linear nonquadratic two-person zero-sum game, and the display expression of the optimal control strategy and the function value of the optimal performance index are given. On the basis of summarizing the content of this paper, the future research direction of stochastic linear two-person zero-sum differential game is discussed.
【学位授予单位】：云南师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O232

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