Stabilizing Transmission Intervals for Nonlinear Delayed Networked Control Systems [Extended Version]

TL;DR

This paper develops a methodology to determine the maximum transmission intervals for nonlinear networked control systems with delays and disturbances, ensuring stability and performance using impulsive system modeling and Lyapunov techniques.

Contribution

It introduces a novel approach combining impulsive delayed system modeling with Lyapunov-Razumikhin methods to compute maximal transmission intervals under various network conditions.

Findings

MATIs can be smaller than communication delays

Method handles variable delays and corrupted data

Numerical examples demonstrate effectiveness

Abstract

In this article, we consider a nonlinear process with delayed dynamics to be controlled over a communication network in the presence of disturbances and study robustness of the resulting closed-loop system with respect to network-induced phenomena such as sampled, distorted, delayed and lossy data as well as scheduling protocols. For given plant-controller dynamics and communication network properties (e.g., propagation delays and scheduling protocols), we quantify the control performance level (in terms of Lp-gains) as the transmission interval varies. Maximally Allowable Transfer Interval (MATI) labels the greatest transmission interval for which a prescribed Lp-gain is attained. The proposed methodology combines impulsive delayed system modeling with Lyapunov-Razumikhin techniques to allow for MATIs that are smaller than the communication delays. Other salient features of our methodology are the consideration of variable delays, corrupted data and employment of model-based estimators to prolong MATIs. The present stability results are provided for the class of Uniformly Globally Exponentially Stable (UGES) scheduling protocols. The well-known Round Robin (RR) and Try-Once-Discard (TOD) protocols are examples of UGES protocols. Finally, two numerical examples are provided to demonstrate the benefits of the proposed approach.