Evolving and Incremental Value Iteration Schemes for Nonlinear Discrete-Time Zero-Sum Games
针对非线性离散时间零和博弈问题，提出了演化与增量值迭代框架，通过引入历史信息调整收敛速度，并验证了其在调节和跟踪问题中的有效性。
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.