Efficient design of low-order H∞ optimal controllers using evolutionary algorithms and a bisection approach

This paper considers a hybrid evolutionaryalgebraic approach to the non-convex problem of designing low-order H
∞
optimal controllers. It is shown that using the closed-loop H
∞
norm as fitness measure in a population-based, evolutionary search does not require the computation of the H
∞
norm for each controller of the population. Instead, the fact that evolutionary algorithms assign fitness measures to individuals based on a ranking is exploited and a bisection approach is proposed that allows to trade accuracy that is not needed against computational efficiency without loosing information. Three design examples are used to illustrate the improvement in computational speed achieved with the proposed method.