Quantized feedback control of continuous time Lur'e systems with nested quantization over finite data rate channels

Abstract

AbstractThis paper studies a control problem of continuous time Lur'e systems involving input quantization (for the output of the controller) and output quantization (for the output of the plant). When the output of one quantization operator becomes directly the input of the other one, the nested quantization is produced, which is difficult for the design of the systems. Based on spherical polar coordinate quantizer, a quantization method with finite data rate is proposed for handling the nested quantization. In addition, both the quantization errors and Lur'e‐type nonlinearity are converted to sector bound uncertainties that are modeled by norm bounded uncertain matrices, which facilitates the design of the systems. Owing to the quantization error the resulting closed‐loop system is described by a discontinuous right‐hand side differential equation and the notion of Krasovskii solution is adopted for the equation. By Krasovskii solution the update rule of the quantization region is designed to ensure the convergence to the origin of the system with the nested quantization and avoid the quantizer saturation. Further, since the quantizers cannot quantize the controller output and the system output directly, we develop an optimalization problem for each quantizer to obtain the estimates of the outputs of the plant and the controller. Finally, a method is presented to achieve the parameters of the controller.