In this paper two types of intelligence supervised controllers are pro
posed with the aim to achieve an overall performance beyond the limit
of linear controllers. In each case, the overall controller has a hier
archical structure with two conventional linear controllers in the bot
tom layer to perform accurate control action under the supervision of
a reasoning process in the top layer. The reasoning process consists o
f heuristic rules drawn from our physical insight, and can easily be i
mplemented either by fuzzy logics or by IF ... THEN statements. Both i
ntelligence supervised controllers achieve a performance beyond the li
mit of linear control laws, and are superior to both a fuzzy controlle
r and a neural controller at least in the sense that their performance
s are independent of the type of command.