Optimal Transmission Power and Controller Design for Networked Control Systems Under State-Dependent Markovian Channels

Bin Hu, Tua Agustinus Tamba

Abstract: 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.