Supervised adaptive PID control and time-varying fuzzy identifier of nonlinear dither systems

To enhance system robustness between system parameters and adaptation law, a supervised adaptive PID control scheme and time-varying fuzzy identifier of unknown nonlinear dither systems are proposed. The dither and the proposed time-varying term can obtain the smooth quality of plant for reducing the rule number of the fuzzy identifier. The supervised adaptive PID control law aims to pull the states back to the pre-specified state region and reduce overshoot towards an extra stabilising input.