IEEE Trans Cybern. 2023 Jul;53(7):4487-4499. doi: 10.1109/TCYB.2022.3198078. Epub 2023 Jun 15.
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.
本文构建了演进式和增量式价值迭代（VI）框架，以解决离散时间零和博弈问题。首先，演进方案意味着闭环系统通过使用演进策略对进行调节。在控制阶段，我们致力于建立稳定性准则，以保证演进策略对的可用性。其次，开发了一种新颖的增量 VI 算法，该算法考虑了迭代过程的历史信息，用于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，突出了我们可以调整迭代代价函数序列的收敛速度。最后，通过两个包括线性和非线性系统的仿真示例，验证了所提出的演进式和增量式 VI 方案的性能和有效性。
