Co-design of Optimal Transmission Power and Controller for Networked Control Systems Under State-dependent Markovian Channels

TL;DR

This paper develops a co-design framework for control and transmission power in networked control systems with state-dependent Markovian channels, ensuring stability and efficiency through novel modeling and optimization techniques.

Contribution

It introduces a new state-dependent Markov channel model and formulates a co-design optimization problem solvable via semidefinite programming for stability and performance.

Findings

Optimal control and power strategies improve system stability.

The proposed methods effectively handle state-dependent fading channels.

Simulation confirms the efficacy of the co-design scheme.

Abstract

This paper considers a co-design problem for industrial networked control systems to ensure both the stability and efficiency properties of such systems. The assurance of such properties 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. To address such challenges, this paper 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 its environment's states and transmission power. Under the proposed channel model, sufficient conditions on Maximum Allowable Transmission Interval (MATI) are presented to ensure both asymptotic stability in expectation and almost sure asymptotic stability properties of a continuous nonlinear control system with state-dependent fading channels. Based on such conditions, the co-design 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 state dependent Markovian channel. 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 still respect the stability constraints. For a general SD-MC model, this paper further shows that sub-optimal solutions can be obtained from linear programming formulations of the considered CPOP. Simulation results are given to illustrate the efficacy of the proposed co-design scheme.