Dynamical Analysis of a Networked Control System

TL;DR

This paper extends the analysis of a network data transmission strategy in control systems by constructing return maps, formulating hybrid models, analyzing stability, and proposing new controller designs to enhance system performance.

Contribution

It generalizes previous work by deriving conditions for periodic orbits, modeling as hybrid systems, analyzing stability, and designing controllers for improved networked control systems.

Findings

Existence conditions for periodic orbits derived.

Hybrid system formulation facilitates analysis.

New controller methods improve network control performance.

Abstract

A new network data transmission strategy was proposed in Zhang \& Chen [2005] (arXiv:1405.2404), where the resulting nonlinear system was analyzed and the effectiveness of the transmission strategy was demonstrated via simulations. In this paper, we further generalize the results of Zhang \& Chen [2005] in the following ways: 1) Construct first-return maps of the nonlinear systems formulated in Zhang \& Chen [2005] and derive several existence conditions of periodic orbits and study their properties. 2) Formulate the new system as a hybrid system, which will ease the succeeding analysis. 3) Prove that this type of hybrid systems is not structurally stable based on phase transition which can be applied to higher-dimensional cases effortlessly. 4) Simulate a higher-dimensional model with emphasis on their rich dynamics. 5) Study a class of continuous-time hybrid systems as the counterparts of the discrete-time systems discussed above. 6) Propose new controller design methods based on this network data transmission strategy to improve the performance of each individual system and the whole network. We hope that this research and the problems posed here will rouse interests of researchers in such fields as control, dynamical systems and numerical analysis.