# Optimal Tracking Performance Limitation of Networked Control Systems with Limited Bandwidth and Additive Colored White Gaussian Noise

## TL;DR

This paper investigates the fundamental limits of tracking performance in networked control systems with bandwidth constraints and colored Gaussian noise, revealing how system zeros, gains, and channel noise affect optimal tracking.

## Contribution

It derives the maximum achievable tracking performance considering bandwidth and noise limitations, providing explicit relationships between system properties and communication channel effects.

## Key findings

- Optimal tracking performance depends on system zeros and gains.
- Limited bandwidth and noise degrade achievable tracking accuracy.
- Simulation confirms theoretical performance bounds.

## Abstract

This paper studies optimal tracking performance issues for multi-input-multi-output linear time-invariant systems under networked control with limited bandwidth and additive colored white Gaussian noise channel. The tracking performance is measured by control input energy and the energy of the error signal between the output of the system and the reference signal with respect to a Brownian motion random process. This paper focuses on two kinds of network parameters, the basic network parameter-bandwidth and the additive colored white Gaussian noise, and studies the tracking performance limitation problem. The best attainable tracking performance is obtained, and the impact of limited bandwidth and additive colored white Gaussian noise of the communication channel on the attainable tracking performance is revealed. It is shown that the optimal tracking performance depends on nonminimum phase zeros, gain at all frequencies and their directions unitary vector of the given plant, as well as the limited bandwidth and additive colored white Gaussian noise of the communication channel. The simulation results are finally given to illustrate the theoretical results.