Predictive control and communication co-design: a Gaussian process regression approach

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the lack of wireless resources, only a limited number of control systems can be served, making the state observations outdated.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 reduces the age-of-information (AoI) of the last received states. Meanwhile, for non-scheduled 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.