Non-conservative adaptive fuzzy sliding mode control for trajectory tracking of non-linear systems

A novel synergetic methodology combining the merits of sliding mode control and fuzzy modelling technique through the modelling-error based adaptive law is developed to solve the trajectory-tracking problem of uncertain non-linear systems. Two modelling-error based adaptive fuzzy systems are utilised to estimate the unknown non-linear systems. Based on the approximation of unknown non-linearities, the equivalent control part of sliding mode control is constructed to adaptively compensate the known part of the uncertainties. Concurrently, a third fuzzy system automatically adjusts the discontinuous gain of switch control to a necessary level in order to overcome the modelling error of the first two fuzzy systems for guaranteeing the reachability of sliding mode. With more knowledge of the uncertainties and acquisition of equivalent control, the switch gain and therefore the chattering can be effectively decreased to the minimum level. The bounds of the uncertainties are not required to be known in advance, and the robust stability of closed loop systems is guaranteed in the Lyapunov sense. Simulation results are given to demonstrate the improved performance.