论文标题
随机自适应线性二次差异游戏
Stochastic Adaptive Linear Quadratic Differential Games
论文作者
论文摘要
游戏理论在理解复杂的系统和研究各种不确定性的智能机器方面发挥了越来越重要的作用。作为起点，我们考虑了经典的两人零和线性界面随机差异游戏，但是与大多数现有研究形成鲜明对比的是，系统的系数矩阵被认为是玩家未知的，因此，它是必不可少的，并且必须研究玩家的适应性策略，这可能被称为适应性游戏和适应性的，这是在自适应上探索的，该策略是在文化中探索的。在本文中，将表明，可以通过加权最小二乘（WLS）估计算法的联合使用来构建两个参与者的自适应策略，一种随机的正则化方法和一种减少的激发方法。在与传统已知参数情况下几乎相同的结构条件下，我们将证明闭环自适应游戏系统将在全球范围内保持稳定，并且渐近地达到NASH平衡，因为时间往往是无限的。
Game theory is playing more and more important roles in understanding complex systems and in investigating intelligent machines with various uncertainties. As a starting point, we consider the classical two-player zero-sum linear-quadratic stochastic differential games, but in contrast to most of the existing studies, the coefficient matrices of the systems are assumed to be unknown to both players, and consequently it is necessary to study adaptive strategies of the players, which may be termed as adaptive games and which has rarely been explored in the literature. In this paper, it will be shown that the adaptive strategies of both players can be constructed by the combined use of a weighted least squares (WLS) estimation algorithm, a random regularization method and a diminishing excitation method. Under almost the same structural conditions as those in the traditional known parameters case, we will show that the closed-loop adaptive game systems will be globally stable and asymptotically reaches the Nash equilibrium as the time tends to infinity.
