In this article, evolving and incremental value iteration (VI) frameworks are constructed to address the discrete-time zero-sum game problem. First, the evolving scheme means that the closed-loop system is regulated by using the evolving policy pair. During the control stage, we are committed to establishing the stability criterion in order to guarantee the availability of evolving policy pairs. Second, a novel incremental VI algorithm, which takes the historical information of the iterative process into account, is developed to solve the regulation and tracking problems for the nonlinear zero-sum game. Via introducing different incremental factors, it is highlighted that we can adjust the convergence rate of the iterative cost function sequence. Finally, two simulation examples, including linear and nonlinear systems, are conducted to demonstrate the performance and the validity of the proposed evolving and incremental VI schemes.

中文翻译：

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非线性离散时间零和博弈的演化和增量值迭代方案

在本文中，构建了演化和增量价值迭代（VI）框架来解决离散时间零和博弈问题。首先，演化方案意味着利用演化策略对来调节闭环系统。在控制阶段，我们致力于建立稳定性标准，以保证不断演化的政策对的可用性。其次，开发了一种考虑迭代过程历史信息的增量VI算法来解决非线性零和博弈的调节和跟踪问题。通过引入不同的增量因子，突出表明我们可以调整迭代成本函数序列的收敛速度。最后，两个仿真示例，包括线性和非线性系统，