Quantized Feedback Control Based on Spherical Polar Coordinate Quantizer

• 成果类型: Article
• 署名作者: Wang, Jian
• 署名单位: Bohai University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3059845
• 发表日期: 2021
• 页码: 6077-6084
• 关键词: Quantization (signal); uncertainty; Robust control; State feedback; Linear systems; Symmetric matrices; Feedback control; Finite data rate; quantized feedback; quantizer; sector bound uncertainty; spherical polar coordinates

摘要

Different from uniform quantizer and logarithmic quantizer, this article proposes a novel quantizer for the design problems of linear systems with quantized feedback. This quantizer is based on spherical polar coordinates and has a desired relation between the quantized vector and the corresponding quantization error. Utilizing the proposed quantizer with infinite data rate, the quadratic stabilization problems of linear systems via state feedback under quantization can be converted, respectively, to the same problems of the corresponding robust control systems with sector bound uncertainties. From a practical point of view, we are more concerned with quantized feedback control with finite data rate, so a quantizer with finite data rate is proposed for the abovementioned problems. Different from the quantizer with infinite data rate, a time-varying bounded quantization region needs to be determined to contain the quantized vector as the system evolves. Under this circumstance, the vector needed to be quantized cannot be quantized directly, so we give a quantization method to solve this problem.