Emulation-based Stabilization for Networked Control Systems with Stochastic Channels

TL;DR

An upper bound on the maximally allowable transmission interval is derived explicitly for all stochastic protocols satisfying Lyapunov conditions that guarantee uniform global asymptotic stability in probability.

Abstract

This paper studies the stabilization problem of networked control systems (NCSs) with random packet dropouts caused by stochastic channels. To describe the effects of stochastic channels on the information transmission, the transmission times are assumed to be deterministic, whereas the packet transmission is assumed to be random. We first propose a stochastic scheduling protocol to model random packet dropouts, and address the properties of the proposed stochastic scheduling protocol. The proposed scheduling protocol provides a unified modelling framework for a general class of random packet dropouts due to different stochastic channels. Next, the proposed scheduling protocol is embedded into the closed-loop system, which leads to a stochastic hybrid model for NCSs with random packet dropouts. Based on this stochastic hybrid model, we follow the emulation approach to establish sufficient conditions to guarantee uniform global asymptotical stability in probability. In particular, an upper bound on the maximally allowable transmission interval is derived explicitly for all stochastic protocols satisfying Lyapunov conditions that guarantee uniform global asymptotic stability in probability. Finally, two numerical examples are presented to demonstrate the derived results.

Figures (4)

• Figure 1: Evolution of the MATI bound $\tau^{\ast}$ with different values of $P_{\mathrm{s}}$ in the RR and TOD cases. The dotted lines are for the deterministic case and the solid curves are for the stochastic case.
• Figure 2: Evolution of the MATI bound $\tau^{\ast}$ with different $\lambda$ and $\rho$ in the RR and TOD cases. Here the probability of transmission success is fixed as $0.8$.
• Figure 3: Illustration of 15 realizations of the state trajectories of the system \ref{['eqn-32']} in the TOD case.
• Figure 4: Illustration of 15 realizations of the state trajectories of the system \ref{['eqn-32']} in the RR case.

Theorems & Definitions (18)

• Definition 1: Subbaraman2016recurrence
• remark 1
• Example 1
• remark 2
• Proposition 1
• proof
• Definition 2
• remark 3
• Proposition 2
• proof