Observer-based quantized output feedback control of nonlinear systems

This paper addresses the problem of stabilizing a nonlinear system by means of quantized output feedback. A framework is presented in which the control input is generated by an observer-based feedback controller acting on quantized output measurements. A stabilization result is established under the assumption that this observer-based controller possesses robustness with respect to output measurement errors in an input-to-state stability (ISS) sense. Designing such observers and controllers is a largely open problem, some partial results on which are discussed. The main goal of the paper is to encourage further work on this important topic.

I. Introduction

The problem studied in this paper is that of stabi-lizing’ in an asymptotic or weaker sense, a nonlinear system using quantized measurements of its output. This problem arises, for example, in the presence of a finite-capacity communication channel between the sensor and the actuator. In this setting, the quantizer models the encoding/decoding scheme used to transmit data along such a channel. Transmitting the output (i.e., a partial measurement of the system state) rather than the full state is not only a necessity in limited-sensing scenarios, but may also be a choice of the designer since this relieves the communication burden. The price to pay, however, is that the missing state information needs to be recovered on the decoder side. Any observer that is employed for this purpose must possess sufficient robustness to the errors affecting the output due to quantization.