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研究了一类带Poisson跳扩散过程的线性二次随机微分博弈,包括非零和博弈的Nash均衡策略与零和博弈的鞍点均衡策略问题.利用微分博弈的最大值原理,得到Nash均衡策略的存在条件等价于两个交叉耦合的矩阵Riccati方程存在解,鞍点均衡策略的存在条件等价于一个矩阵Riccati方程存在解的结论,并给出了均衡策略的显式表达及最优性能泛函值.最后,将所得结果应用于现代鲁棒控制中的随机H_2/H_∞控制与随机H_∞控制问题,得到了鲁棒控制策略的存在条件及显式表达,并验证所得结果在金融市场投资组合优化问题中的应用.
A class of linear stochastic differential game with Poisson jump diffusion process is studied, including Nash equilibrium strategy of non-zero sum game and saddle point equilibrium strategy of zero-sum game. Using the maximum value principle of differential game, the existence of Nash equilibrium strategy The condition is equivalent to the existence of solution of two cross-coupled matrix Riccati equations. The existence condition of saddle-point equilibrium strategy is equivalent to the existence of solution of a matrix Riccati equation. The explicit expression of the equilibrium strategy and the optimal functional of function Finally, the results are applied to the random H 2 / H ∞ control and stochastic H ∞ control problems in modern robust control, the existence conditions and explicit expressions of the robust control strategy are obtained, and the results obtained in the financial market portfolio Application in optimization problem.