GENETIC SOLUTIONS TO MIXED H2/H∞ PROBLEMS - Limits of Performance

Abstract

One of the most relevant problems for control engineers is the so-called "mixed H 2 /H ∞ ". To solve it, different convexifying strategies became popular in the later 1990s, mainly based on Linear Matrix Inequalities (LMIs). On the other hand, genetic algorithms have also been applied for H 2 /H ∞ synthesis. Indeed, several authors agree that they are able to find good solutions to this important control problem. However, in most of the published papers, only low-order SISO models have been considered. In the present paper a LMI-based algorithm is compared against a genetic algorithm, with respect to three performance indicators: Set Coverage, Maximum Distance and Efficient Set Spacing. Five open-loop MIMO models extracted from COMPl e ib are studied, for which the degree varies between 5 and 10. Based on numerical results, the genetic algorithm is not able to improve LMI solutions for problems with more than 42 variables, restricted to a budget of 20.000 function evaluations.