Wireless networked control systems (WNCSs) require the design of a robust scheduling algorithm that meets the stringent timing and reliability requirements of control systems, despite the limited battery resources of sensor nodes and adverse properties of wireless communication for delay and packet errors. In this article, we propose a robust delay and energy constrained scheduling algorithm based on the exploitation of the mostly pre-known periodic data generation nature of sensor nodes in control systems. We first formulate the joint optimization of scheduling, power control and rate adaptation for discrete rate transmission model, in which only a finite set of transmission rates are supported, as a Mixed-Integer Non-linear Programming problem and prove its NP-hardness. Next, we propose an optimal polynomial-time power control and rate adaptation algorithm for minimizing the transmission time of a node subset. We then design a novel polynomial-time heuristic scheduling algorithm based on first determining the concurrently transmitting node subsets and then distributing them uniformly over time by a modified Karmarkar-Karp algorithm. We demonstrate the superior performance of the proposed scheduling algorithm in terms of robustness, delay and runtime on the Low-Rate Wireless Personal Area Network (LR-WPAN) simulation platform, which we developed in network simulator-3 (ns3).

无线网络控制系统（WNCS）要求设计鲁棒的调度算法，以满足传感器系统的严格定时和可靠性要求，尽管传感器节点的电池资源有限，并且无线通信的延迟和数据包错误具有不利的特性。在本文中，我们基于对控制系统中传感器节点的最著名的周期性数据生成性质的利用，提出了一种鲁棒的延迟和能量受限调度算法。首先，我们将仅支持有限传输速率集的离散速率传输模型的调度，功率控制和速率自适应联合优化设计为混合整数非线性规划问题，并证明了其NP难度。下一个，我们提出了一种最优的多项式时间功率控制和速率自适应算法，以最小化节点子集的传输时间。然后，我们基于改进的Karmarkar-Karp算法，首先确定并发传输的节点子集，然后将它们随时间均匀分布，然后设计一种新颖的多项式时间启发式调度算法。我们在低速率无线个人局域网（LR-WPAN）仿真平台上展示了​​所提出的调度算法在鲁棒性，延迟和运行时间方面的优越性能，该平台是我们在网络模拟器3（ns3）中开发的。然后，我们基于改进的Karmarkar-Karp算法，首先确定并发传输的节点子集，然后将它们随时间均匀分布，然后设计一种新颖的多项式时间启发式调度算法。我们在低速率无线个人局域网（LR-WPAN）仿真平台上展示了​​所提出的调度算法在鲁棒性，延迟和运行时间方面的优越性能，该平台是我们在网络模拟器3（ns3）中开发的。然后，我们基于改进的Karmarkar-Karp算法，首先确定并发传输的节点子集，然后将它们随时间均匀分布，然后设计一种新颖的多项式时间启发式调度算法。我们在低速率无线个人局域网（LR-WPAN）仿真平台上展示了​​所提出的调度算法在鲁棒性，延迟和运行时间方面的优越性能，该平台是我们在网络模拟器3（ns3）中开发的。