Real-time remote control over wireless is an important yet challenging application in fifth-generation and beyond due to its mission-critical nature under limited communication resources. Current solutions hinge on not only utilizing ultrareliable and low-latency communication (URLLC) links but also predicting future states, which may consume enormous communication resources and struggle with a short prediction time horizon. To fill this void, in this article we propose a novel two-way Koopman autoencoder (AE) approach wherein: 1) a sensing Koopman AE learns to understand the temporal state dynamics and predicts missing packets from a sensor to its remote controller and 2) a controlling Koopman AE learns to understand the temporal action dynamics and predicts missing packets from the controller to an actuator co-located with the sensor. Specifically, each Koopman AE aims to learn the Koopman operator in the hidden layers while the encoder of the AE aims to project the nonlinear dynamics onto a lifted subspace, which is reverted into the original nonlinear dynamics by the decoder of the AE. The Koopman operator describes the linearized temporal dynamics, enabling long-term future prediction and coping with missing packets and closed-form optimal control in the lifted subspace. Simulation results corroborate that the proposed approach achieves a $38\times $ lower mean squared control error at 0-dBm signal-to-noise ratio (SNR) than the nonpredictive baseline.

中文翻译：

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通过无线双向拆分 Koopman 自编码器进行预测性闭环远程控制

无线实时远程控制是第五代及以后的一项重要但具有挑战性的应用，因为它在有限的通信资源下具有关键任务性质。当前的解决方案不仅取决于利用超可靠和低延迟通信 (URLLC) 链接，而且还取决于预测未来状态，这可能会消耗大量通信资源并在较短的预测时间范围内挣扎。为了填补这一空白，在本文中，我们提出了一种新颖的双向 Koopman 自动编码器 (AE) 方法，其中：1) 传感 Koopman AE 学习理解时间状态动态并预测从传感器到其远程控制器的丢失数据包，以及 2)控制 Koopman AE 学习理解时间动作动态，并预测从控制器到与传感器位于同一位置的执行器的丢失数据包。具体来说，每个 Koopman AE 旨在学习隐藏层中的 Koopman 算子，而 AE 的编码器旨在将非线性动力学投影到提升的子空间上，该子空间由 AE 的解码器恢复为原始非线性动力学。Koopman 算子描述线性化的时间动态，支持长期未来预测和处理丢失的数据包以及提升子空间中的封闭形式最优控制。仿真结果证实了所提出的方法实现了 在提升的子空间中实现长期未来预测和处理丢失的数据包和封闭形式的最优控制。仿真结果证实了所提出的方法实现了 在提升的子空间中实现长期未来预测和处理丢失的数据包和封闭形式的最优控制。仿真结果证实了所提出的方法实现了 $38\次 $0 dBm 信噪比 (SNR) 的均方控制误差低于非预测性基线。