Abstract

In filtering, control, and other mathematical engineering areas it is common to use a model-based approach, which splits the problem into two steps: 1) model identification and 2) model-based design. Despite its success, the model-based approach has the shortcoming that the design objective is not taken into account at the identification step, i.e., the model is not optimized for its intended use. In this talk, I show a data-driven approach, which combines the identification and the model-based design into one joint problem. The signal of interest is modeled as a missing part of a trajectory of the data generating system. Subsequently, the missing data estimation problem is reformulated as a mosaic-Hankel structured matrix low-rank approximation/completion problem.

The missing data estimation approach for data-driven signal processing and a local optimization method for its practical implementation are illustrated on examples of control, state estimation, filtering/smoothing, and prediction. Development of fast algorithms with provable properties in the presence of measurement noise and disturbances is a topic of current research.

Reference: I. Markovsky. A missing data approach to data-driven filtering and control. IEEE Trans. Automat. Contr., 2017. http://homepages.vub.ac.be/~imarkovs/publications/ddsp.pdf