Lexicographic tuning of a fuzzy controller using Box´s `complex´ algorithm

A fuzzy control system typically requires tuning, or adjustment, of the parameters defining its linguistic variables. Automating this process amounts to applying a second metacontrol layer to drive the controller and plant to desired performance levels. Current methods of automated tuning rely on a single crisp numeric functional to evaluate control system performance. The methodology employed does not assume that the controllable factors and the performance variable have continuous numerical values. A generalization of Box´s complex algorithm allows more realistic tuning based on lexicographic aggregation of multiple ordinal scales of performance, such as effectiveness and efficiency. The method is presented and illustrated using a simple inverted-pendulum control system