Direct search methods for an open problem of optimization in systems and control

TL;DR

This paper compares traditional iterative linear matrix inequality algorithms with general purpose optimization solvers for control system optimization problems, demonstrating the latter's superior performance and broader applicability.

Contribution

It highlights the limitations of ILMI algorithms and advocates for the use of general purpose optimization methods in control system optimization tasks.

Findings

General purpose solvers outperform ILMI in the considered problem.

ILMI lacks guaranteed global convergence.

Broader applicability of general optimization methods in control problems.

Abstract

The motivation of this work is to illustrate the efficiency of some often overlooked alternatives to deal with optimization problems in systems and control. In particular, we will consider a problem for which an iterative linear matrix inequality algorithm (ILMI) has been proposed recently. As it often happens, this algorithm does not have guaranteed global convergence and therefore many methods may perform better. We will put forward how some general purpose optimization solvers are more suited than the ILMI. This is illustrated with the considered problem and example, but the general observations remain valid for many similar situations in the literature.