Data-Driven Control of Linear Systems via Quantized Feedback

Quantized feedback control is fundamental to system synthesis with limited communication capacity. In sharp contrast to the existing literature on quantized control which requires an explicit dynamical model, the authors study the quadratic stabilization and performance control problems with logarithmically quantized feedback in a direct data-driven framework, where the system state matrix is not exactly known and instead, belongs to an ambiguity set that is directly constructed from a finite number of noisy system data. To this end, the authors firstly establish sufficient and necessary conditions via linear matrix inequalities for the existence of a common quantized controller that achieves our control objectives over the ambiguity set. Then, the authors provide necessary conditions on the data for the solvability of the LMIs, and determine the coarsest quantization density via semi-definite programming. The theoretical results are validated through numerical examples.