Networked control systems: a perspective from chaos

TL;DR

This paper explores a nonlinear networked control system with chaotic dynamics, analyzing its stability, bifurcations, and control methods, demonstrating complex behaviors and potential for reduced signal transmission.

Contribution

It introduces a nonlinear control system with chaos properties, providing detailed stability analysis and control strategies within networked control systems.

Findings

System exhibits local stability, non-origin equilibrium, periodic, and oscillatory behaviors.

System shows sensitive dependence on initial conditions, indicating chaos.

An example demonstrates the effectiveness of the control scheme.

Abstract

In this paper, a nonlinear system aiming at reducing the signal transmission rate in a networked control system is constructed by adding nonlinear constraints to a linear feedback control system. Its stability is investigated in detail. It turns out that this nonlinear system exhibits very interesting dynamical behaviors: in addition to local stability, its trajectories may converge to a non-origin equilibrium or be periodic or just be oscillatory. Furthermore it exhibits sensitive dependence on initial conditions --- a sign of chaos. Complicated bifurcation phenomena are exhibited by this system. After that, control of the chaotic system is discussed. All these are studied under scalar cases in detail. Some difficulties involved in the study of this type of systems are analyzed. Finally an example is employed to reveal the effectiveness of the scheme in the framework of networked control systems.