This article studies the joint problem of uplink-downlink scheduling and power allocation for controlling a large number of control systems that upload their states to remote controllers and download control actions over wireless links. To overcome the lack of wireless resources, we propose a machine learning-based solution, where only one control system is controlled, while the rest of the control systems are actuated by locally predicting the missing state and/or action information using the previous uplink and/or downlink receptions via a Gaussian process regression (GPR). This GPR prediction credibility is determined using the age-of-information (AoI) of the latest reception. Moreover, the successful reception is affected by the transmission power, mandating a co-design of the communication and control operations. To this end, we formulate a network-wide minimization problem of the average AoI and transmission power under communication reliability and control stability constraints. To solve the problem, we propose a dynamic control algorithm using the Lyapunov drift-plus-penalty optimization framework. Numerical results corroborate that the proposed algorithm can stably control 2x more number of actuators compared to an event-triggered scheduling baseline with Kalman filtering and frequency division multiple access, which is 18x larger than a round-robin scheduling baseline.

While Remote control over wireless connections is a key enabler for scalable control systems consisting of multiple actuator-sensor pairs, i.e., control systems, it entails two technical challenges. Due to the lack of wireless resources, only a limited number of control systems can be served, making the state observations outdated. Further, even after scheduling, the state observations received through wireless channels are distorted, hampering control stability. To address these issues, in this article we propose a scheduling algorithm that guarantees the age-ofinformation (AoI) of the last received states. Meanwhile, for nonscheduled sensor-actuator pairs, we propose a machine learning (ML) aided predictive control algorithm, in which states are predicted using a Gaussian process regression (GPR). Since the GPR prediction credibility decreases with the AoI of the input data, both predictive control and AoI-based scheduler should be co-designed. Hence, we formulate a joint scheduling and transmission power optimization via the Lyapunov optimization framework. Numerical simulations corroborate that the proposed co-designed predictive control and AoI based scheduling achieves lower control errors, compared to a benchmark scheme using a round-robin scheduler without state prediction. Index Terms-Predictive control, age of information, communication and control co-design, Gaussian process regression.

Remote state monitoring over wireless is envisaged to play a pivotal role in enabling beyond 5G applications ranging from remote drone control to remote surgery. One key challenge is to identify the system dynamics that is non-linear with a large dimensional state. To obviate this issue, in this article we propose to train an autoencoder whose encoder and decoder are split and stored at a state sensor and its remote observer, respectively. This autoencoder not only decreases the remote monitoring payload size by reducing the state representation dimension but also learns the system dynamics by lifting it via a Koopman operator, thereby allowing the observer to locally predict future states after training convergence. Numerical results under a non-linear cartpole environment demonstrate that the proposed split learning of a Koopman autoencoder can locally predict future states, and the prediction accuracy increases with the representation dimension and transmission power.

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