direct adaptive fuzzy pi sliding mode control of systems with unknown but bounded disturbances

an asymptotically stable direct adaptive fuzzy pi sliding modecontroller is proposed for a class of nonlinear uncertain systems. in contrast toother existing approaches of handling disturbances, the proposed approachdoes not require this bound to be known, only requiring that it exists.moreover, a pi control structure is used to attenuate chattering. the approachis applied to stabilize an open-loop unstable nonlinear system as well asthe duffing forced-oscillation chaotic nonlinear system amid significantdisturbances. analysis of simulations reveals the effectiveness of the proposedmethod in terms of a significant reduction in chattering while maintainingasymptotic convergence.