This article considers a codesign problem for industrial networked control systems to ensure both stability and efficiency properties of such systems. This problem is particularly challenging due to the fact that wireless communications in industrial environments are not only subject to shadow fading, but also stochastically correlated with their surrounding environments. This article first introduces a novel state-dependent Markov channel (SD-MC) model that explicitly captures the state-dependent features of industrial wireless communication systems by defining the proposed model’s transition probabilities as a function of both environments’ states and transmission power. Under the SD-MC model, sufficient conditions on Maximum Allowable Transmission Interval are presented to ensure both asymptotic stability in expectation and almost sure asymptotic stability properties of a nonlinear control system with state-dependent fading channels. Based on these stability conditions, the codesign problem is then formulated as a constrained polynomial optimization problem (CPOP), which can be efficiently solved using semidefinite programming methods for the case of a two-state SD-MC model. The solutions to such a CPOP represent optimal control and power strategies that optimize the average expected joint costs in an infinite time horizon while respecting the stability constraints. For a general SD-MC model, this article further shows that suboptimal solutions can be obtained from linear programming formulations of the considered CPOP. Simulation results are given to illustrate the efficacy of the proposed codesign scheme.

中文翻译：

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状态相关马尔可夫通道下网络控制系统的最优传输功率和控制器设计


本文考虑工业网络控制系统的协同设计问题，以确保此类系统的稳定性和效率。这个问题尤其具有挑战性，因为工业环境中的无线通信不仅会受到阴影衰落的影响，而且还与周围环境随机相关。本文首先介绍了一种新颖的状态相关马尔可夫信道 (SD-MC) 模型，该模型通过将模型的转移概率定义为环境状态和传输功率的函数，明确捕获工业无线通信系统的状态相关特征。在SD-MC模型下，给出了最大允许传输间隔的充分条件，以确保具有状态相关衰落信道的非线性控制系统的期望渐近稳定性和几乎确定的渐近稳定性。基于这些稳定性条件，协同设计问题被表述为约束多项式优化问题（CPOP），对于二态 SD-MC 模型的情况，可以使用半定规划方法有效地求解。这种 CPOP 的解决方案代表了最优控制和功率策略，可在无限时间范围内优化平均预期联合成本，同时尊重稳定性约束。对于一般的 SD-MC 模型，本文进一步表明，可以从所考虑的 CPOP 的线性规划公式中获得次优解。仿真结果说明了所提出的协同设计方案的有效性。