The use of fractional calculus can improve and generalize well-established control methods and strategies.
[1] The fundamental advantage of FOC is that the fractional-order integrator weights history using a function that decays with a power-law tail.
, in the sense that it is a non-local operator that possesses an infinite memory and takes into account the whole history of its input signal.
Fractional-order control has also been demonstrated to be capable of suppressing chaotic behaviors in mathematical models of, for example, muscular blood vessels[3] and robotics.
Oustaloup's group, the CRONE approach[clarification needed] is one of the most developed control-system design methodologies that uses fractional-order operator properties.