Improved prescribed performance constraint control for a strict feedback non-linear dynamic system

An improved prescribed performance control using a backstepping technique and adaptive fuzzy is proposed for a strict feedback nonlinear dynamic system. A new virtual variable was defined to generate the virtual control that forces the tracking errors to fall within prescribed boundaries, and an adaptive fuzzy system was used to obtain required approximation performances. A strict feedback controller and adaptive laws for estimating the unknown non-linear function were designed to avoid a singularity problem and calculation of the explosive number of terms generated by the error transformations of conventional error constraint method and the recursive steps of traditional backstepping control. Lyapunov stability analysis confirmed the boundedness and convergence of the closed-loop system. The prescribed error constraint performance of the proposed control scheme was validated by applying it to control the position of a second-order non-linear system and a robot manipulator.