# Optimal Tracking Performance of Control Systems with Two-Channel Constraints

## TL;DR

This paper investigates the fundamental limits of tracking performance in networked control systems with dual-channel constraints, considering bandwidth, noise, and plant complexities, and proposes optimal control strategies.

## Contribution

It provides a comprehensive theoretical framework for understanding how channel and plant constraints jointly affect optimal tracking performance in NCSs.

## Key findings

- Optimal tracking performance is limited by plant zeros, poles, and channel noise.
- Performance bounds depend on bandwidth, noise, and plant characteristics.
- Simulation confirms theoretical performance limitations.

## Abstract

This paper focuses on the tracking performance limitation for a class of networked control systems(NCSs) with two-channel constraints. In communication channels, we consider bandwidth, energy constraints and additive colored Gaussian noise(ACGN) simultaneously. In plant, non-minimal zeros and unstable poles are considered; multi-repeated zeros and poles are also applicable. To obtain the optimal performance, the two-parameter controller is adopted. The theoretical results show that the optimal tracking performance is influenced by the non-minimum phase zeros, unstable poles, gain at all frequencies of the given plant, and the reference input signal for NCSs. Moreover, the performance limitation is also affected by the limited bandwidth, additive colored Gaussian noise, and the corresponding multiples for the non-minimum phase zeros and unstable poles. Additionally, the channel minimal input power constraints are given under the condition ensuring the stability of the system and acquiring system performance limitation. Finally, simulation examples are given to illustrate the theoretical results.