With the wide use of networks in repetitive systems, channels between a plant and a controller may experience random fading, which is a common problem in long-distance wireless communication. However, the control problem over fading channels is far from resolved. In this article, we investigate learning control over fading channels to gradually improve tracking performance. We observe that the effect of fading on input transmission greatly compromises tracking ability in practical implementations. We examine three average techniques: moving average, general average with all historical information, and forgetting-based average. The results reveal a tradeoff between learning ability and tracking ability for learning control algorithms, where learning ability refers to the convergence rate of a proposed learning algorithm, and tracking ability refers to the final tracking precision of the output to the desired reference. The convergence results for the three schemes with these averaging techniques are strictly proved. The results demonstrate that the forgetting-based average operator-based scheme can connect the other two schemes by tuning the forgetting factor. We also provide extensions of several general scenarios to expand the application range. Illustrative simulations verify the theoretical results.

中文翻译：

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平衡衰落通道学习和跟踪能力的平均技术


随着网络在重复系统中的广泛使用，设备和控制器之间的信道可能会遇到随机衰落，这是长距离无线通信中的常见问题。然而，衰落信道的控制问题还远未得到解决。在本文中，我们研究了对衰落通道的学习控制，以逐步提高跟踪性能。我们观察到，衰落对输入传输的影响极大地损害了实际实现中的跟踪能力。我们研究三种平均技术：移动平均、包含所有历史信息的综合平均以及基于遗忘的平均。结果揭示了学习控制算法的学习能力和跟踪能力之间的权衡，其中学习能力是指所提出的学习算法的收敛速度，而跟踪能力是指输出到期望参考的最终跟踪精度。严格证明了使用这些平均技术的三种方案的收敛结果。结果表明，基于平均算子的遗忘方案可以通过调整遗忘因子来连接其他两种方案。我们还提供了几种通用场景的扩展，以扩大应用范围。说明性模拟验证了理论结果。