Development of data-based controller synthesis by convex optimization

Recently, many researches extracting an essence from a huge number of data receive much attention in the various field of engineering. In the field of control engineering, the controller syntheses from time-domain and/or frequency domain data are energetically studied based on numerical optimization techniques. This paper presents a recent development of data-based controller synthesis by convex optimization, and shows that a special case of nonconvex optimization problems, which is often encountered in the control field, is reformulated as a convex optimization problem by introducing the concave-convex procedure or the Iterated LMI constraints. As an application, the H infinity loop shaping design procedure reformulated using frequency response data of a controlled plant is presented.