论文标题
关于在零和随机差游戏中产生的广义riccati方程的稳定解决方案的存在：随时间变化的情况
On the existence of the stabilizing solution of generalized Riccati equations arising in zero sum stochastic difference games: The time-varying case
论文作者
论文摘要
在本文中，考虑了在随机动态游戏中产生的大量时变的Riccati方程。研究了某些全球定义解决方案的存在和唯一性的问题，即有界和稳定的解决方案。作为所获得的存在结果的应用，我们在第二步中解决了无限 - 摩恩零和两个播放器的问题，两个播放器线性二次（LQ）动态游戏，用于随机切换其系数和多样性噪声的随机离散时间动态系统。我们表明，在解决此类最佳控制问题的解决方案中，由所考虑的广义Riccati方程的独特界面和稳定解决方案发挥了至关重要的作用。
In this paper, a large class of time-varying Riccati equations arising in stochastic dynamic games is considered. The problem of the existence and uniqueness of some globally defined solution, namely the bounded and stabilizing solution, is investigated. As an application of the obtained existence results, we address in a second step the problem of infinite-horizon zero-sum two players linear quadratic (LQ) dynamic game for a stochastic discrete-time dynamical system subject to both random switching of its coefficients and multiplicative noise. We show that in the solution of such an optimal control problem, a crucial role is played by the unique bounded and stabilizing solution of the considered class of generalized Riccati equations.
