Event-Driven Control for NCSs with Logarithmic Quantization and Packet Losses

Jingjing Yan

doi:10.1155/2017/7592825

Abstract

The stabilization problem of the networked control systems (NCSs) affected by data quantization, packet losses, and event-driven communication is studied in this paper. By proposing two event-driven schemes and the extended forms of them relying on quantized states, zoom strategy is adopted here to study the system stability with time-varying logarithmic quantization and independent identically distributed (IID) packet losses process. On the basis of that, some sufficient conditions ensuring the mean square stability of the system are obtained here. Although zoom strategy has been utilized by many literatures to study the quantized stabilization problem of NCSs, it has not been adopted to analyze the stability of NCSs with data quantization, IID packet losses, and event-driven communication. Furthermore, the existing literatures relating to zoom strategy employ the quantizer with quantization regions holding arbitrary shapes, but here we use the logarithmic quantizer which holds better performance near the origin. In addition, the detailed comparisons of the system performance under different event-driven schemes are given here, which can guide the strategy selection according to the different design goals. The above three points are the main innovations of this paper. At last, the effectiveness of the proposed methods is illustrated by a benchmark example.

Highlights

The introduction of the network in the control system brings us a lot of convenience, such as increased flexibility and maintainability and reduced wiring cost
Network inserted in the control system brings some new challenges for studying the stability and stabilization problems of the closed-loop system
Under the network-induced imperfections including data quantization, transmission delay, packet losses, and communication constraints, the sampled signals can not be transmitted timely and accurately through the network, which results in the fact that the system performance may be degraded, or even instability

Summary

Introduction

The introduction of the network in the control system brings us a lot of convenience, such as increased flexibility and maintainability and reduced wiring cost. By restraining the upper bound of the number of successive packet losses and adopting the logarithmic quantization strategy proposed in [25, 26], the sufficient conditions ensuring the asymptotical stability of the systems are shown in [23], in which an event-driven scheme is designed by the errors between the current sampling states and the last transmitted states. Considering the advantages of the logarithmic quantizer, such as which holds better performance near the origin, we adopt zoom strategy to handle the stabilization problem for NCSs with logarithmic quantization, packet losses, and event-driven communication. It is worth mentioning that the logarithmic quantization combined with zoom strategy has already been studied in our paper [28], but in which the packet losses and event-driven scheme are all uncovered. Zero vector with dimension n × 1 is denoted as 0n×1

Problem Formulation

Network Formulation

Analysis and Comparison

Simulation

Conclusion