Explicit formula of hedge-algebras-based fuzzy controller and applications in structural vibration control

In the present work, explicit formula or mathematical model of hedge-algebras-based controller (HAC) is proposed to represent relationship between control and state variables. In contrast to a conventional fuzzy controller (FC), when using Hedge Algebras (HA) theory to design HACs, their explicit formula or mathematical model can be expressed in term of a simple equation. Applications of HAC using the explicit formula in input time-delay and sliding-mode controls are also studied. Control performance of HACs is investigated by numerical simulations on active control of a building structure subjected to earthquake excitations, in which results obtained from the FC are also included for comparison.