We analyze the closed-loop control performance of a networked control system that consists of $N$ independent linear feedback control loops, sharing a communication network with $M$ channels ($M<N$). A centralized scheduler, employing a scheduling protocol that produces periodic communication sequences, dictates which feedback loops should utilize all these channels. Under the periodic scheduling protocol, we derive analytical expressions for quantifying the overall control performance of the networked control system in terms of a quadratic function. We also formulate the offline combinatorial optimization of communication sequences for a given collection of linear feedback control subsystems. Then, we apply Monte Carlo Tree Search to determine the period of these communication sequences that attain near-optimal control performance. Via numerical studies, we show the effectiveness of the proposed framework.
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