Optimal Networked Control Systems with State-dependent Markov Channels

This paper considers a co-design problem for industrial networked control systems to ensure both system stability and resources efficiency. Solving such a co-design problem is challenging because wireless communications in industrial environments are subject to shadow fading, and are stochastically correlated with their surrounding environments. To address such challenges, this paper first introduces a novel state-dependent Markov channel model that explicitly captures the state-dependent features of the wireless communications by correlating model's transition probabilities with environment states. Under the proposed channel model, sufficient conditions on maximum allowable transmission interval are presented to ensure almost sure asymptotic stability for a nonlinear networked control system. With the stability constraints, the co-design problem is then formulated as constrained optimization problems, which can be efficiently solved by Semidefinite programs for a two-state Markov channel. Simulation results are provided to demonstrate the efficacy of the proposed co-design scheme.