Recent years have seen several new directions in the design of sparse control of cyber–physical systems (CPSs) driven by the objective of reducing communication costs. One common assumption made in these designs is that the communication happens over a dedicated network. For many practical applications, however, communication must occur over shared networks, leading to two critical design challenges, namely — time-delays in the feedback and fair sharing of bandwidth among users. In this paper, we present a set of sparse ${\mathcal{H}}_2$ control designs under these two design constraints. An essential aspect of our design is that the delay itself can be a function of sparsity, which leads to an interesting pattern of trade-offs in the ${\mathcal{H}}_2$ performance. We present three distinct algorithms. The first algorithm preconditions the assignable bandwidth to the network and produces an initial guess for a stabilizing controller. This is followed by our second algorithm, which sparsifies this controller while simultaneously adapting the feedback delay and optimizing the ${\mathcal{H}}_2$ performance using alternating directions method of multipliers (ADMM). The third algorithm extends this approach to a multiple user scenario where an optimal number of communication links, whose total sum is fixed, is distributed fairly among users by minimizing the variance of their ${\mathcal{H}}_2$ performances. The problem is cast as a difference-of-convex (DC) program with mixed-integer linear program (MILP) constraints. We provide theorems to prove the convergence of these algorithms, followed by validation through numerical simulations.

近年来，在降低通信成本的目标驱动下，稀疏控制网络物理系统（CPS）的设计出现了几个新的方向。这些设计中的一个普遍假设是通信是通过专用网络进行的。但是，对于许多实际应用而言，通信必须通过共享网络进行，这带来了两个关键的设计挑战，即-反馈中的时间延迟和用户之间带宽的公平共享。在本文中，我们提出了一套稀疏${\mathcal{H}}_2$在这两个设计约束下控制设计。我们设计的一个重要方面是，延迟本身可能是稀疏性的函数，这导致了一个有趣的折衷模式。${\mathcal{H}}_2$性能。我们提出了三种不同的算法。第一种算法会为网络分配可分配的带宽，并为稳定控制器产生初始猜测。其次是我们的第二种算法，该算法稀疏了该控制器，同时调整了反馈延迟并优化了${\mathcal{H}}_2$使用交替方向乘数法（ADMM）的性能。第三种算法将该方法扩展到多用户方案，在该方案中，通过使用户的方差最小化，可以在用户之间公平分配最佳数量的通信链路（其总和是固定的）${\mathcal{H}}_2$表演。该问题被转换为具有混合整数线性程序（MILP）约束的凸差（DC）程序。我们提供定理来证明这些算法的收敛性，然后通过数值模拟进行验证。