信息与控制2016，Vol.45Issue(3)：257-265,9.DOI:10.13976/j.cnki.xk.2016.0257
带Poisson跳的线性二次随机微分博弈及其在鲁棒控制中的应用
Linear Quadratic Stochastic Differential Games with Poisson Jumps and Their Application to Robust Control
摘要
Abstract
In this paper,we investigate a class of linear quadratic stochastic differential games with a Poisson jumps diffusion process,including the Nash equilibrium strategies of a nonzero sum game and the saddle point equilibrium strategies of a zero sum game.Utilizing the maximum principle for differential games,we determine that the existence conditions of the Nash equilibrium strategies are equivalent to the solution for two cross-coupled matrix Riccati equations,and that the existence conditions of the saddle point equilibrium strategies are equivalent to the solution for a matrix Riccati equation.We also provide explicit expressions for the equilibrium strategy and the optimal performance functional value.Finally,we apply the obtained results to problems dealing with stochastic H2/H∞ control and stochastic H∞ control in the fields of modern robust control theory,and obtain the existence conditions of robust control strategies and their explicit expressions.Moreover,we verify the performance of these results in a financial market portfolio optimisation problem.关键词
随机微分博弈/矩阵Riccati方程/随机H2/H∞控制Key words
stochastic differential games/matrix Riccati equation/stochastic H2/H∞ control分类
管理科学引用本文复制引用
张成科,曹铭,朱怀念,朱莹,程硕..带Poisson跳的线性二次随机微分博弈及其在鲁棒控制中的应用[J].信息与控制,2016,45(3):257-265,9.基金项目
国家自然科学基金资助项目(71171061,71571053) （71171061,71571053）
中国博士后科学基金资助项目(2014M552177) （2014M552177）
广东省自然科学基金项目(2014A030310366,2015A030310218) （2014A030310366,2015A030310218）
广东工业大学校青年基金资助项目(14QND002) （14QND002）
