Data-driven Filter Design for Linear Systems with Quantized Measurements

This paper is concerned with the problem of data-driven filter design for linear systems with bounded noise by using quantized measurements. Since the mathematical model of the plant studied is unavailable, most of the existing model-based filter design approaches cannot be used to solve this problem. Another challenge lies in the fact that all the measurement data accessible is quantized. To solve this issue, a quasi-feasible filter set within the set membership framework is proposed, and a data-driven optimal worst-case filter is designed. Furthermore, an l2-l∞ almost-optimal worst-case filter design algorithm is presented by means of linear programming technique. A numerical example is given to illustrate the effectiveness of the proposed algorithms.