We investigate the trade-off between controllability, channel access, and age-related performance in a wireless network of control systems. Controllers share a random-access channel to transmit control inputs to actuators over slotted blocks. We measure reliable control via block controllability, where a block is controllable if it contains a required number of consecutive successful transmissions. In parallel, we capture information freshness via the age of information. To enable efficient allocation of channel resources over time, we introduce adaptive access probabilities at the block level, prioritizing controllers that have not yet achieved controllability. We then derive closed-form expressions for block controllability probability, the peak latency between inter-block consecutive successes, and peak age of information. We further characterize the peak control latency, defined as the time between consecutive controllable blocks. Finally, we optimize access probabilities to jointly balance controllability and age-related metrics. Numerical results illustrate the effectiveness of the proposed adaptive access policies in managing this trade-off in interference-limited wireless control networks.

翻译：我们研究了无线控制系统网络中可控性、信道接入与时效性能之间的权衡关系。控制器通过共享随机接入信道，在分时隙数据块上向执行器传输控制指令。采用数据块可控性衡量可靠控制性能——当数据块包含所需数量的连续成功传输时，即视为该数据块可控。同时，通过信息年龄表征信息新鲜度。为优化信道资源的时域分配，我们在数据块层级引入自适应接入概率，优先服务尚未达成可控性的控制器。进而推导出数据块可控概率、数据块间连续成功传输的峰值延迟以及信息峰值年龄的闭式表达式。进一步刻画了峰值控制延迟，定义为连续可控数据块之间的时间间隔。最后，通过优化接入概率实现可控性与时效指标的联合均衡。数值结果验证了所提出的自适应接入策略在干扰受限无线控制网络中管理该权衡关系的有效性。