Dynamic output feedback under quantization based on spherical polar coordinate quantizer

Abstract

Different from uniform quantizer and logarithmic quantizer, this article utilizes a novel quantizer based on spherical polar coordinates for the design problems of quantized feedback systems with dynamic output feedback. This quantizer has a desired relation between the quantized vector and the corresponding quantization error, by which in this article the quantization error is converted to the uncertainty of the systems and stabilization problems of linear systems via dynamic output feedback under quantization can be converted to the corresponding robust control problems. From a practical point of view, we are concerned with quantized feedback control with finite data rate and use the quantizer with finite data rate to design quantized feedback systems. Under the quantizer with finite data rate, a time‐varying bounded quantization region needs to be determined to contain the quantized vector as the system evolves. Under this circumstance, some entries of the quantized vector are not available to the quantizer with finite data rate such that the vector cannot be quantized directly, so we propose a quantization and controller design method to solve this problem.

Finite‐level uniformly quantized learning control with random data dropouts

“…The choice of quantizer has also become a critical issue. To name a few, logarithmic quantizer, 18,[26][27][28] uniform quantizer, [29][30][31][32] probabilistic quantizer, 33,34 and quantizer based on spherical polar coordinate [35][36][37] are used to quantify data before transmission. Generally, a uniform quantizer would be more practical than others in applications because of its cheapness and availability.…”